A geometric inequality for stable solutions of semilinear elliptic problems in the Engel group

Andrea Pinamonti, Enrico Valdinoci

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

We prove that, if E is the Engel group and u is a stable solution of ΔEu = f(u), then for any test function η ∈ C0 (E). Here above, h is the horizontal mean curvature, p is the imaginary curvature and J:= 2(X3X2uX1u - X3X1uX2u) + (X4u)(X1u - X2u) This can be interpreted as a geometric Poincaré inequality, extending the work of [21,22, 13] to stratified groups of step 3. As an application, we provide a non-existence result.

Original languageEnglish
Pages (from-to)357-373
Number of pages17
JournalAnnales Academiae Scientiarum Fennicae Mathematica
Volume37
Issue number1
DOIs
Publication statusPublished - 1 Jan 2012
Externally publishedYes

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