Hardy-Rellich inequalities with boundary remainder terms and applications

DOI10.1007/s00229-009-0328-6zbMath1187.35045OpenAlexW2050734112WikidataQ59278480 ScholiaQ59278480MaRDI QIDQ2268173

Elvise Berchio, Gazzola, Filippo, Daniele Cassani

Publication date: 10 March 2010

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00229-009-0328-6

zbMATH Keywords

extremal solutionsHardy-Rellich inequalitiesSteklov boundary conditionsbiharmonic Gelfand-type equations

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Inequalities involving derivatives and differential and integral operators (26D10) Variational methods for higher-order elliptic equations (35J35)

Related Items (18)

Hardy-Rellich inequalities in domains of the Euclidean space ⋮ Periodic solutions to nonlocal MEMS equations ⋮ Hardy-Rellich identities with Bessel pairs ⋮ Scaling invariant Hardy type inequalities with non-standard remainder terms ⋮ Hardy and Hardy–Rellich type inequalities with Bessel pairs ⋮ Qualitative behavior of global solutions to some nonlinear fourth order differential equations ⋮ The first biharmonic Steklov eigenvalue: positivity preserving and shape optimization ⋮ Estimates of Hardy - Rellich constants for polyharmonic operators and their generalizations ⋮ Existence and stability of entire solutions to a semilinear fourth order elliptic problem ⋮ A note on the Rellich inequality on half-space ⋮ Global existence for nonlocal MEMS ⋮ Rellich type inequalities with weights in plane domains ⋮ A note on the second order geometric Rellich inequality on half-space ⋮ Improved Hardy and Hardy-Rellich type inequalities with Bessel pairs via factorizations ⋮ On some higher order Hardy-Rellich type inequalities with boundary terms ⋮ On solutions of second and fourth order elliptic equations with power-type nonlinearities ⋮ Improved Rellich Type Inequalities in $${\mathbb {R}}^{N}$$ ⋮ Some Results Concerning Hardy and Hardy Type Inequalities

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Bessel pairs and optimal Hardy and Hardy-Rellich inequalities
• The critical dimension for a fourth-order elliptic problem with singular nonlinearity
• Supercritical biharmonic equations with power-type nonlinearity
• Positivity preserving property for a class of biharmonic elliptic problems
• Entire solutions for a semilinear fourth order elliptic problem with exponential nonlinearity
• Optimal Hardy--Rellich inequalities, maximum principle and related eigenvalue problem
• Best constants in the Hardy-Rellich inequalities and related improvements
• The Dirichlet problem for supercritical biharmonic equations with power-type nonlinearity
• On positivity for the biharmonic operator under Steklov boundary conditions
• Multiplicity of solutions for a fourth order equation with power-type nonlinearity
• Best constants for higher-order Rellich inequalities in \(L^{p}(\Omega )\)
• On the first eigenvalue of a fourth order Steklov problem
• On solutions of second and fourth order elliptic equations with power-type nonlinearities
• Multiplicity of solutions for a fourth order problem with exponential nonlinearity
• Regularity of the extremal solution for a biharmonic problem with general nonlinearity
• Some continuation and variational methods for positive solutions of nonlinear elliptic eigenvalue problems
• Remarks on the Schrödinger operator with singular complex potentials
• Explicit constants for Rellich inequalities in \(L_p(\Omega)\)
• A simple approach to Hardy inequalities
• Positive solutions in semilinear critical problems for polyharmonic operators
• Best constant for the embedding of the space \(H^ 2\cap H^ 1_ 0(\Omega)\) into \(L^{2N/(N-4)}\Omega\)
• Radial entire solutions for supercritical biharmonic equations
• On a class of Rellich inequalities
• Quasilinear Dirichlet problems driven by positive sources
• On a Fourth Order Nonlinear Elliptic Equation with Negative Exponent
• On a fourth order Steklov eigenvalue problem
• The singular extremal solutions of the bi-Laplacian with exponential nonlinearity
• On a Fourth Order Elliptic Problem with a Singular Nonlinearity
• Direct and inverse problems related to MEMS
• Sur une classe de problemes non lineaires avec non linearite positive, croissante, convexe.
• Hardy inequalities with optimal constants and remainder terms
• A Semilinear Fourth Order Elliptic Problem with Exponential Nonlinearity
• Compactness along the branch of semistable and unstable solutions for an elliptic problem with a singular nonlinearity
• Nonlinear non-local elliptic equation modelling electrostatic actuation
• Stable Solutions for the Bilaplacian with Exponential Nonlinearity
• Critical dimensions and higher order Sobolev inequalities with remainder terms

This page was built for publication: Hardy-Rellich inequalities with boundary remainder terms and applications