Asymptotic symmetry and local behaviors of solutions to a class of anisotropic elliptic equations

DOI10.1512/iumj.2011.60.4376zbMath1388.35060OpenAlexW2093767691MaRDI QIDQ4899227

Zhi-Qiang Wang, Chun-Hsiung Hsia, Chang-Shou Lin

Publication date: 7 January 2013

Published in: Indiana University Mathematics Journal (Search for Journal in Brave)

Full work available at URL: http://www.iumj.indiana.edu/IUMJ/ABS/2011/4376

zbMATH Keywords

Caffarelli-Kohn-Nirenberg inequalitymoving planes methodHardy-Sobolev inequality

Mathematics Subject Classification ID

Critical exponents in context of PDEs (35B33) Semilinear elliptic equations (35J61) Positive solutions to PDEs (35B09) Symmetries, invariants, etc. in context of PDEs (35B06)

Related Items (14)

A unified approach to symmetry for semilinear equations associated to the Laplacian in \(\mathbb{R}^N\) ⋮ On Delaunay solutions of a biharmonic elliptic equation with critical exponent ⋮ Finite Morse index solutions of weighted elliptic equations and the critical exponents ⋮ Classification to the positive radial solutions with weighted biharmonic equation ⋮ Expansions for distributional solutions of the elliptic equation in two dimensions ⋮ Existence and regularity of positive solutions of a degenerate elliptic problem ⋮ Structure of minimizers of Cafarelli-Kohn-Nirenberg inequality ⋮ Qualitative analysis of singular solutions for nonlinear elliptic equations with potentials ⋮ Further study of a weighted elliptic equation ⋮ Monotonicity formula and \(\varepsilon\)-regularity of stable solutions to supercritical problems and applications to finite Morse index solutions ⋮ Weighted fourth order elliptic problems in the unit ball ⋮ Bôcher-type results for the fourth and higher order equations on singular manifolds with conical metrics ⋮ Existence of sharp asymptotic profiles of singular solutions to an elliptic equation with a sign-changing non-linearity ⋮ Asymptotic behavior at the isolated singularities of solutions of some equations on singular manifolds with conical metrics

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