Nonexistence of local solutions to semilinear partial differential inequalities

We investigate nonexistence of local nonnegative solutions for some semilinear elliptic and parabolic inequalities with first order terms and singular coefficients. In contrast with previous investigations of the subject, no use of the maximum principle is made. Instead, a direct bootstrap argument...

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Bibliographic Details
Published inAnnales de l'Institut Henri Poincaré. Analyse non linéaire Vol. 21; no. 4; pp. 487 - 502
Main Authors Pohozaev, Stanislav I, Tesei, Alberto
Format Journal Article
LanguageEnglish
Published Elsevier Masson SAS 01.08.2004
Subjects
Instantaneous blow-up
Local solutions
Nonexistence
Partial differential inequalities
35D05
Solutions locales
Instantaneous blow-up
Partial differential inequalities
35J60
Nonexistence
Explosion instantanée
Inégalités aux dérivées partielles
Local solutions
35K55
Non existence
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Summary:We investigate nonexistence of local nonnegative solutions for some semilinear elliptic and parabolic inequalities with first order terms and singular coefficients. In contrast with previous investigations of the subject, no use of the maximum principle is made. Instead, a direct bootstrap argument is used, which relies on a suitable choice of the functions used to test the differential inequalities. Nous étudions la non existence de solutions locales non négatives pour quelques inégalités elliptiques et paraboliques avec termes du premier ordre et coefficients singuliers. Au lieu de méthodes faisant appel au principe du maximum, on utilise une méthode directe de “bootstrap” basée sur un choix convenable des fonctions test.
ISSN:0294-1449
1873-1430
DOI:10.1016/j.anihpc.2003.06.002