JournalsaihpcVol. 21, No. 4pp. 487–502

Nonexistence of local solutions to semilinear partial differential inequalities

  • Stanislav I Pohozaev

    Steklov Mathematical Institute, Russian Academy of Sciences, Gubkina 8, 117966 Moscow, Russia
  • Alberto Tesei

    Dipartimento di Matematica “G. Castelnuovo”, Università di Roma “La Sapienza”, P.le A. Moro 5, 00185 Roma, Italy
Nonexistence of local solutions to semilinear partial differential inequalities cover
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Abstract

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.

Résumé

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.

Cite this article

Stanislav I Pohozaev, Alberto Tesei, Nonexistence of local solutions to semilinear partial differential inequalities. Ann. Inst. H. Poincaré Anal. Non Linéaire 21 (2004), no. 4, pp. 487–502

DOI 10.1016/J.ANIHPC.2003.06.002