Regularity and nonexistence results for anisotropic quasilinear elliptic equations in convex domains

Pages: 280 - 286, Issue Special, August 2005

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Ilaria Fragalà - Dipartimento di Matematica - Politecnico, Piazza Leonardo Da Vinci 32, 20133, Milano, Italy (email)
Filippo Gazzola - Dipartimento di Matematica Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133 Milano, Italy (email)
Gary Lieberman - Department of Mathematics, Iowa State University, Ames, IA 50011, United States (email)

Abstract: For a class of anisotropic elliptic problems in bounded domains $\Omega$ we show that the convexity of $\Omega$ plays an important role in regularity and nonexistence results. Using recent results in [9] we improve some statements in [3].

Keywords:  Anisotropic Sobolev spaces, critical exponents, a-starshaped domains, Poho·zaev identity.
Mathematics Subject Classification:  Primary: 35J70, 46E35; Secondary: 35B65.

Received: September 2004;      Revised: May 2005;      Published: September 2005.