The precise boundary trace of solutions of a class of supercritical nonlinear equations

Moshe Marcus; Laurent Véron

doi:10.1016/j.crma.2006.11.028

Partial Differential Equations

The precise boundary trace of solutions of a class of supercritical nonlinear equations
[La trace au bord précise des solutions d'une classe d'équations non linéaires sur-critiques]

Présenté par : Haïm Brezis

Moshe Marcus ¹ ; Laurent Véron ²

¹ Department of Mathematics, Technion, Haifa 32000, Israel
² Laboratoire de mathématiques et physique théorique, faculté des sciences, parc de Grandmont, 37200 Tours, France

Comptes Rendus. Mathématique, Volume 344 (2007) no. 3, pp. 181-186.

Résumé
Abstract

Nous construisons et étudions les propriétés de la trace au bord précise des solutions positives de $- Δ u + u^{q} = 0$ dans un domaine régulier de $R^{N}$ , dans le cas sur-critique $q ⩾ q_{c} = (N + 1) / (N - 1)$ .

We construct and study the properties of the precise boundary trace of positive solutions of $- Δ u + u^{q} = 0$ in a smooth bounded domain of $R^{N}$ , in the supercritical case $q ⩾ q_{c} = (N + 1) / (N - 1)$ .

Accepté le : 2006-11-14
Publié le : 2006-12-21

DOI : 10.1016/j.crma.2006.11.028

Affiliations des auteurs :

Moshe Marcus ¹ ; Laurent Véron ²

¹ Department of Mathematics, Technion, Haifa 32000, Israel
² Laboratoire de mathématiques et physique théorique, faculté des sciences, parc de Grandmont, 37200 Tours, France

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     title = {The precise boundary trace of solutions of a class of supercritical nonlinear equations},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {181--186},
     publisher = {Elsevier},
     volume = {344},
     number = {3},
     year = {2007},
     doi = {10.1016/j.crma.2006.11.028},
     language = {en},
}

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Moshe Marcus; Laurent Véron. The precise boundary trace of solutions of a class of supercritical nonlinear equations. Comptes Rendus. Mathématique, Volume 344 (2007) no. 3, pp. 181-186. doi : 10.1016/j.crma.2006.11.028. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.11.028/

Bibliographie
Cité par

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[4] E.B. Dynkin; S.E. Kuznetsov Superdiffusions and removable singularities for quasilinear partial differential equations, Comm. Pure Appl. Math., Volume 49 (1996), pp. 125-176

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[9] M. Marcus; L. Véron The boundary trace of positive solutions of semilinear elliptic equations: the subcritical case, Arch. Rat. Mech. Anal., Volume 144 (1998), pp. 201-231

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