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- Deprecated function: Return type of DatabaseStatementBase::execute($args = [], $options = []) should either be compatible with PDOStatement::execute(?array $params = null): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in require_once() (line 2244 of /home/laurentp/www/includes/database/database.inc).
- Deprecated function: Return type of DatabaseStatementEmpty::current() should either be compatible with Iterator::current(): mixed, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in require_once() (line 2346 of /home/laurentp/www/includes/database/database.inc).
- Deprecated function: Return type of DatabaseStatementEmpty::next() should either be compatible with Iterator::next(): void, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in require_once() (line 2346 of /home/laurentp/www/includes/database/database.inc).
- Deprecated function: Return type of DatabaseStatementEmpty::key() should either be compatible with Iterator::key(): mixed, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in require_once() (line 2346 of /home/laurentp/www/includes/database/database.inc).
- Deprecated function: Return type of DatabaseStatementEmpty::valid() should either be compatible with Iterator::valid(): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in require_once() (line 2346 of /home/laurentp/www/includes/database/database.inc).
- Deprecated function: Return type of DatabaseStatementEmpty::rewind() should either be compatible with Iterator::rewind(): void, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in require_once() (line 2346 of /home/laurentp/www/includes/database/database.inc).
- Deprecated function: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in drupal_random_bytes() (line 2268 of /home/laurentp/www/includes/bootstrap.inc).
- Deprecated function: Optional parameter $type declared before required parameter $key is implicitly treated as a required parameter in include_once() (line 1389 of /home/laurentp/www/includes/bootstrap.inc).
- Deprecated function: Return type of DateObject::__wakeup() should either be compatible with DateTime::__wakeup(): void, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in include_once() (line 143 of /home/laurentp/www/sites/all/modules/date/date_api/date_api.module).
- Deprecated function: Return type of DateObject::format($format, $force = false) should either be compatible with DateTime::format(string $format): string, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in include_once() (line 143 of /home/laurentp/www/sites/all/modules/date/date_api/date_api.module).
- Deprecated function: Return type of DateObject::setTimezone($tz, $force = false) should either be compatible with DateTime::setTimezone(DateTimeZone $timezone): DateTime, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in include_once() (line 143 of /home/laurentp/www/sites/all/modules/date/date_api/date_api.module).
- Deprecated function: Optional parameter $input declared before required parameter $form_state is implicitly treated as a required parameter in include_once() (line 1389 of /home/laurentp/www/includes/bootstrap.inc).
- Deprecated function : Creation of dynamic property SelectQuery::$alterTags is deprecated dans SelectQuery->addTag() (ligne 978 dans /home/laurentp/www/includes/database/select.inc).
- Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
- Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
- Deprecated function : Creation of dynamic property SelectQuery::$alterMetaData is deprecated dans SelectQuery->addMetaData() (ligne 997 dans /home/laurentp/www/includes/database/select.inc).
- Deprecated function : Creation of dynamic property SelectQuery::$alterTags is deprecated dans SelectQuery->addTag() (ligne 978 dans /home/laurentp/www/includes/database/select.inc).
- Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
- Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
- Deprecated function : Creation of dynamic property SelectQuery::$alterMetaData is deprecated dans SelectQuery->addMetaData() (ligne 997 dans /home/laurentp/www/includes/database/select.inc).
- Deprecated function : Creation of dynamic property SelectQuery::$alterTags is deprecated dans SelectQuery->addTag() (ligne 978 dans /home/laurentp/www/includes/database/select.inc).
- Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
- Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
- Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
- Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
- Deprecated function : rtrim(): Passing null to parameter #1 ($string) of type string is deprecated dans url() (ligne 2349 dans /home/laurentp/www/includes/common.inc).
- Deprecated function : strlen(): Passing null to parameter #1 ($string) of type string is deprecated dans _filter_url_trim() (ligne 1664 dans /home/laurentp/www/modules/filter/filter.module).
- Deprecated function : Creation of dynamic property SelectQuery::$alterTags is deprecated dans SelectQuery->addTag() (ligne 978 dans /home/laurentp/www/includes/database/select.inc).
- Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
- Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
- Deprecated function : Creation of dynamic property SelectQuery::$alterTags is deprecated dans SelectQuery->addTag() (ligne 978 dans /home/laurentp/www/includes/database/select.inc).
- Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
- Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
- Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
- Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
- Deprecated function : Creation of dynamic property PDOException::$query_string is deprecated dans DatabaseConnection->query() (ligne 770 dans /home/laurentp/www/includes/database/database.inc).
- Deprecated function : Creation of dynamic property PDOException::$args is deprecated dans DatabaseConnection->query() (ligne 772 dans /home/laurentp/www/includes/database/database.inc).
- Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
- Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
- Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
- Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
- Deprecated function : strpos(): Passing null to parameter #1 ($haystack) of type string is deprecated dans url_is_external() (ligne 2393 dans /home/laurentp/www/includes/common.inc).
- Deprecated function : str_replace(): Passing null to parameter #3 ($subject) of type array|string is deprecated dans url_is_external() (ligne 2395 dans /home/laurentp/www/includes/common.inc).
- Deprecated function : ltrim(): Passing null to parameter #1 ($string) of type string is deprecated dans url() (ligne 2311 dans /home/laurentp/www/includes/common.inc).
- Deprecated function : Creation of dynamic property SelectQuery::$alterTags is deprecated dans SelectQuery->addTag() (ligne 978 dans /home/laurentp/www/includes/database/select.inc).
- Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
- Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
- Deprecated function : Creation of dynamic property SelectQuery::$alterTags is deprecated dans SelectQuery->addTag() (ligne 978 dans /home/laurentp/www/includes/database/select.inc).
- Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
- Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
- Deprecated function : Creation of dynamic property SelectQuery::$alterTags is deprecated dans SelectQuery->addTag() (ligne 978 dans /home/laurentp/www/includes/database/select.inc).
- Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
- Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
- Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
- Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
- Deprecated function : Creation of dynamic property SelectQuery::$alterTags is deprecated dans SelectQuery->addTag() (ligne 978 dans /home/laurentp/www/includes/database/select.inc).
- Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
- Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
- Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
- Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
- Deprecated function : Creation of dynamic property SelectQuery::$alterTags is deprecated dans SelectQuery->addTag() (ligne 978 dans /home/laurentp/www/includes/database/select.inc).
- Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
- Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
- Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
- Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
- Deprecated function : Creation of dynamic property SelectQuery::$alterTags is deprecated dans SelectQuery->addTag() (ligne 978 dans /home/laurentp/www/includes/database/select.inc).
- Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
- Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
- Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
- Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
- Deprecated function : Creation of dynamic property SelectQuery::$alterTags is deprecated dans SelectQuery->addTag() (ligne 978 dans /home/laurentp/www/includes/database/select.inc).
- Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
- Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
Analyse fonctionelle
Soumis par Laurent Petit cours le dim, 12/08/2012 - 10:12
Titre | Analyse fonctionelle |
Type de publication | Livre |
Année de Publication | 1986 |
Auteurs | Brezis H |
Series Title | Mathématiques appliquées pour la maitrise |
Edition | Masson |
Number of Pages | 233 |
Date de Publication | 12/1986 |
Éditeur | Masson |
Ville | Paris |
Mots-Clés | compacité faible, dualité, EDP, hilbert, Hille Yosida, réflexif, sobolev, unifomément convexe |
Résumé | Un exposé très clair sur l'analyse fonctionnelle dans l'optique de la résolution d'équation aux dérivées partielles, l'axiome du choix non dénombrable est assumé. Topologie faible, espaces réflexifs et séparables.Espaces de Hilbert. Espaces Lp et de Sobolev. Résolution d'EDP par méthode variationnelle, en invoquant la compacité. Régularité des solutions ainsi trouvées. |
Reprint Edition | 2e |
Citation Key | Brezis |
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