Nonexistence results for elliptic equations with supercritical growth in thick planar domains

Abstract

In this paper, we give some examples of non-star-shaped bounded domains of ${\mathbb{R}}^2$ where, for a class of nonlinear elliptic Dirichlet problems involving supercritical Sobolev exponents, there exists only the trivial identically zero solution (notice that a well-known result of Pohozaev concerns only the star-shaped domains).
Unlike the case of previous papers (Molle and Passaseo (2020, 2021, 2023, 2025)) where we proved nonexistence results for nontrivial solutions in thin domains sufficiently close to prescribed curves, in the present paper, the domains do not need to be thin.