Asymmetric Poincaré inequalities and solvability of capillarity problems

DOI10.1016/j.jfa.2014.03.011zbMath1328.46033OpenAlexW2032500640MaRDI QIDQ2253213

Franco Obersnel, Sabrina Rivetti, Pierpaolo Omari

Publication date: 25 July 2014

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2014.03.011

zbMATH Keywords

existencemultiplicityPoincaré inequalitymean curvaturenon-existenceLandesman-Lazer conditionnon-smooth critical point theorybounded variation functionAhmad-Lazer-Paul conditionHammerstein conditioncapillarity equation

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Absolutely continuous real functions of several variables, functions of bounded variation (26B30) Quasilinear elliptic equations with mean curvature operator (35J93)

Related Items (10)

Minimization to the Zhang's energy on \(BV (\Omega)\) and sharp affine Poincaré-Sobolev inequalities ⋮ Paths to uniqueness of critical points and applications to partial differential equations ⋮ Regular versus singular solutions in quasilinear indefinite problems with sublinear potentials ⋮ Positive solutions of indefinite logistic growth models with flux-saturated diffusion ⋮ Positive solutions of superlinear indefinite prescribed mean curvature problems ⋮ Global components of positive bounded variation solutions of a one-dimensional indefinite quasilinear Neumann problem ⋮ Positive solutions of a one-dimensional indefinite capillarity-type problem: a variational approach ⋮ Revisiting the sub- and super-solution method for the classical radial solutions of the mean curvature equation ⋮ Optimal regularity results for the one-dimensional prescribed curvature equation via the strong maximum principle ⋮ Bifurcation of positive solutions for a one-dimensional indefinite quasilinear Neumann problem

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