Data di Pubblicazione:
2020
Citazione:
Symmetry results for critical anisotropic p-Laplacian equations in convex cones / G. Ciraolo, A. Figalli, A. Roncoroni. - In: GEOMETRIC AND FUNCTIONAL ANALYSIS. - ISSN 1016-443X. - 30:3(2020 Jun 01), pp. 770-803. [10.1007/s00039-020-00535-3]
Abstract:
Given n≥ 2 and 1 < p< n, we consider the critical p-Laplacian equation Δpu+up∗-1=0, which corresponds to critical points of the Sobolev inequality. Exploiting the moving planes method, it has been recently shown that positive solutions in the whole space are classified. Since the moving plane method strongly relies on the symmetries of the equation and the domain, in this paper we provide a new approach to this Liouville-type problem that allows us to give a complete classification of solutions in an anisotropic setting. More precisely, we characterize solutions to the critical p-Laplacian equation induced by a smooth norm inside any convex cone. In addition, using optimal transport, we prove a general class of (weighted) anisotropic Sobolev inequalities inside arbitrary convex cones.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Convex cones; Qualitative properties; Quasilinear anisotropic elliptic equations; Sobolev embedding
Elenco autori:
G. Ciraolo, A. Figalli, A. Roncoroni
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