[Symmetry of large solutions of semilinear elliptic equations]
Let g be a locally Lipschitz continuous function defined on . We assume that g satisfies the Keller–Osserman condition and there exists a positive real number a such that g is convex on . Then any solution u of in a ball B of , , which tends to infinity on ∂B, is spherically symmetric.
Soit g une fonction localement lipschitzienne de la variable réelle. On suppose que g vérifie la condition de Keller et Osserman et qu'il existe un réel tel que g est convexe sur . Alors toute solution u de dans une boule B de , , qui tend vers l'infini au bord de B, est une fonction radiale.
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Alessio Porretta 1; Laurent Véron 2
@article{CRMATH_2006__342_7_483_0, author = {Alessio Porretta and Laurent V\'eron}, title = {Sym\'etrie des grandes solutions d'\'equations elliptiques semi lin\'eaires}, journal = {Comptes Rendus. Math\'ematique}, pages = {483--487}, publisher = {Elsevier}, volume = {342}, number = {7}, year = {2006}, doi = {10.1016/j.crma.2006.01.020}, language = {fr}, }
Alessio Porretta; Laurent Véron. Symétrie des grandes solutions d'équations elliptiques semi linéaires. Comptes Rendus. Mathématique, Volume 342 (2006) no. 7, pp. 483-487. doi : 10.1016/j.crma.2006.01.020. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.01.020/
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