Symmetry and uniqueness of nonnegative solutions of some problems in the halfspace

DOI10.1016/j.jmaa.2013.02.048zbMath1283.35039arXiv1212.0516OpenAlexW2014016217MaRDI QIDQ394943

Alberto Farina, Nicola Soave

Publication date: 28 January 2014

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1212.0516

zbMATH Keywords

Fourier seriesLiouville theorems1-D symmetry for elliptic problemsuniqueness for elliptic problems

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Symmetries, invariants, etc. in context of PDEs (35B06) Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs (35B53)

Related Items (7)

Some results about semilinear elliptic problems on half-spaces ⋮ Nonnegative solutions of semilinear elliptic equations in half-spaces ⋮ On fractional elliptic equations in Lipschitz sets and epigraphs: regularity, monotonicity and rigidity results ⋮ Qualitative properties and classification of nonnegative solutions to \(-\Delta u=f(u)\) in unbounded domains when \(f(0) < 0\) ⋮ Monotonicity and symmetry of nonnegative solutions to \(-\Delta u=f(u)\) in half-planes and strips ⋮ Monotonicity of solutions for some nonlocal elliptic problems in half-spaces ⋮ The Dirichlet problem for \(-\Delta\varphi = \mathrm{e}^{- \varphi}\) in an infinite sector. Application to plasma equilibria

Cites Work

• Some remarks on half space problems
• Flattening results for elliptic PDEs in unbounded domains with applications to overdetermined problems
• A priori bounds for positive solutions of nonlinear elliptic equations
• Some notes on the method of moving planes
• Symmetry of the blow‐up set of a porous medium type equation
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