On polyharmonic regularizations of \(k\)-Hessian equations: variational methods

DOI10.1016/j.na.2015.06.004zbMath1330.35115arXiv1507.05435OpenAlexW2963977167MaRDI QIDQ495266

Yong-Cai Geng, Sumit K. Garg

Publication date: 9 September 2015

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1507.05435

zbMATH Keywords

existence of solutionsvariational methodsmultiplicity of solutionshigher order elliptic equations\(k\)-Hessian type equations

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Variational methods for higher-order elliptic equations (35J35)

Related Items (12)

Existence and multiplicity of radial solutions for a \(k\)-Hessian system ⋮ Polyharmonic \(k\)-Hessian equations in \(\mathbb{R}^N\) ⋮ The Keller-Osserman problem for the k-Hessian operator ⋮ Explicit blowing up solutions for a higher order parabolic equation with Hessian nonlinearity ⋮ Existence of \(k\)-convex solutions for the \(k\)-Hessian equation ⋮ Existence results for the \(k\)-Hessian type system with the gradients via \(\mathbb{R}_+^n\)-monotone matrices ⋮ The extreme solutions for a σ‐Hessian equation with a nonlinear operator ⋮ Radial solutions of a nonlinear \(k\)-Hessian system involving a nonlinear operator ⋮ Unnamed Item ⋮ Existence and nonexistence of radial solutions of the Dirichlet problem for a class of general k-Hessian equations ⋮ Classification and existence of positive entire \(k\)-convex radial solutions for generalized nonlinear \(k\)-Hessian system ⋮ Existence of radial solutions to biharmonic \(k\)-Hessian equations

Cites Work

• Radial fractional Laplace operators and Hessian inequalities
• The Jacobian determinant revisited
• On the distributional Jacobian of maps from \(\mathbb{S}^N\) into \(\mathbb{S}^N\) in fractional Sobolev and Hölder spaces
• The critical dimension for a fourth-order elliptic problem with singular nonlinearity
• Supercritical biharmonic equations with power-type nonlinearity
• On the theory of harmonic functions of several variables
• The Dirichlet problem for supercritical biharmonic equations with power-type nonlinearity
• Interior \(W^{2,p}\) estimates for solutions of the Monge-Ampère equation
• Polyharmonic boundary value problems. Positivity preserving and nonlinear higher order elliptic equations in bounded domains
• Multiplicity of solutions for a fourth order equation with power-type nonlinearity
• The Dirichlet problem for nonlinear second order elliptic equations. III: Functions of the eigenvalues of the Hessian
• Hessian measures. I
• On the optimality of certain Sobolev exponents for the weak continuity of determinants
• Hardy space estimates for multilinear operators. I
• Hardy space estimates for multilinear operators. II
• On the integrability of the Jacobian under minimal hypotheses
• Existence of multiple solutions to the equations of Monge-Ampère type
• Convexity conditions and existence theorems in nonlinear elasticity
• A local version of real Hardy spaces
• Integrability for the Jacobian of orientation preserving mappings
• On the singular support of the distributional determinant
• On the Dirichlet problem for Hessian equations
• A Poincaré type inequality for Hessian integrals
• Global existence versus blow-up results for a fourth order parabolic PDE involving the Hessian
• On the variational principle
• Potential estimates for a class of fully nonlinear elliptic equations.
• Hessian measures. III
• \({\mathcal H}^1\)-estimates of Jacobians by subdeterminants
• Degree theory of BMO. I: Compact manifolds without boundaries
• Compensated compactness and Hardy spaces
• On a new class of elastic deformations not allowing for cavitation
• A note on weak approximation of minors
• Some fourth order nonlinear elliptic problems related to epitaxial growth
• Hessian measures. II
• Dual variational methods in critical point theory and applications
• Existence of radial solutions to biharmonic \(k\)-Hessian equations
• Degree theory and BMO. II: Compact manifolds with boundaries. (Appendix with Petru Mironescu)
• Boundary regularity for the Monge-Ampère and affine maximal surface equations
• The Yamabe problem for higher order curvatures
• Weak convergence of completely additive vector functions on a set
• The Dirichlet Problem for Degenerate Hessian Equations
• Higher integrability of determinants and weak convergence in L1.
• Multiplicity of Solutions for Elliptic Problems with Critical Exponent or with a Nonsymmetric Term
• Existence results for a fourth order partial differential equation arising in condensed matter physics
• The singular extremal solutions of the bi-Laplacian with exponential nonlinearity
• The k-Hessian Equation
• The dirichlet problem for nonlinear second-order elliptic equations I. Monge-ampégre equation
• Hardy spaces, BMO, and boundary value problems for the Laplacian on a smooth domain in 𝐑^{𝐍}
• Some Counterexamples to the Regularity of Monge-Ampere Equations
• Weak solutions of hessian equations
• On locally convex hypersurfaces with boundary
• A variational theory of the Hessian equation
• On radial stationary solutions to a model of non-equilibrium growth
• A Semilinear Fourth Order Elliptic Problem with Exponential Nonlinearity
• Origins of scaling relations in nonequilibrium growth
• Existence and nonexistence results for a singular boundary value problem arising in the theory of epitaxial growth
• Stable Solutions for the Bilaplacian with Exponential Nonlinearity
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: On polyharmonic regularizations of \(k\)-Hessian equations: variational methods