Monotonicity and symmetry results for \(p\)-Laplace equations and applications

zbMath1002.35045MaRDI QIDQ5954452

Filomena Pacella, Lucio Damascelli

Publication date: 4 February 2002

Published in: Advances in Differential Equations (Search for Journal in Brave)

zbMATH Keywords

Sobolev embeddingsclassical isoperimetric inequalitygrowth conditionsymmetry theorem of Serrin

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Maximum principles in context of PDEs (35B50) Degenerate elliptic equations (35J70) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05)

Related Items (29)

Asymptotic estimates and blow-up theory for critical equations involving the \(p\)-Laplacian ⋮ Monotonicity and symmetry of positive solution for 1-Laplace equation ⋮ Variational formula and overdetermined problem for the principal eigenvalue of \(k\)-Hessian operator ⋮ Faber-Krahn inequality for Robin problems involving \(p\)-Laplacian ⋮ A priori estimates for some elliptic equations involving the \(p\)-Laplacian ⋮ The \(p\)-Laplacian overdetermined problem on Riemannian manifolds ⋮ Multiple weak solutions for pi(x)‐Kirchhoff‐type quasilinear elliptic systems ⋮ A new symmetry criterion based on the distance function and applications to PDE's ⋮ Uniqueness and nondegeneracy for some nonlinear elliptic problems in a ball. ⋮ Existence and qualitative properties of solutions to a quasilinear elliptic equation involving the Hardy-Leray potential ⋮ Equivalence between uniform \(L^{p^*}\) a priori bounds and uniform \(L^\infty\) a priori bounds for subcritical \(p\)-Laplacian equations ⋮ Symmetry results for overdetermined problems on convex domains via Brunn-Minkowski inequalities ⋮ An overdetermined problem for a weighted Poisson's equation ⋮ Partially overdetermined elliptic boundary value problems ⋮ Uniqueness of solutions to singular \(p\)-Laplacian equations with subcritical nonlinearity ⋮ Structure of least-energy solutions for quasilinear elliptic equations on convex domains ⋮ Factorization into \(k\)-bubbles for Palais-Smale maps to potential type energy functionals ⋮ Existence and a priori estimates for positive solutions of \(p\)-Laplace systems ⋮ Regularity, monotonicity and symmetry of positive solutions of \(m\)-Laplace equations ⋮ On the Faber–Krahn inequality for the Dirichletp-Laplacian ⋮ Overdetermined problems with possibly degenerate ellipticity, a geometric approach ⋮ Global solution branches for \(p\)-Laplacian boundary value problems ⋮ On the Poisson equation of \(p\)-Laplacian and the nonlinear Hardy-type problems ⋮ The soap bubble theorem and a \(p \)-Laplacian overdetermined problem ⋮ Asymptotic behaviour, nodal lines and symmetry properties for solutions of superlinear elliptic equations near an eigenvalue ⋮ Radial symmetry forp-harmonic functions in exterior and punctured domains ⋮ The overdetermined problem and lower bound estimate on the first nonzero Steklov eigenvalue of \(p\)-Laplacian ⋮ A symmetry result for an overdetermined elliptic problem using continuous rearrangement and domain derivative ⋮ Symmetry and stability of non-negative solutions to degenerate elliptic equations in a ball

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