1D symmetry for solutions of semilinear and quasilinear elliptic equations

Alberto Farina, Enrico Valdinoci

Research output: Contribution to journalArticle

21 Citations (Scopus)


Several new 1D results for solutions of possibly singular or degenerate elliptic equations, inspired by a conjecture of De Giorgi, are provided. In particular, 1D symmetry is proven under the assumption that either the profiles at infinity are 2D, or that one level set is a complete graph, or that the solution is minimal or, more generally, Q-minimal.

Original languageEnglish
Pages (from-to)579-609
Number of pages31
JournalTransactions of the American Mathematical Society
Issue number2
Publication statusPublished - 1 Feb 2011
Externally publishedYes


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