On the existence of Wp2 solutions for fully nonlinear elliptic equations under either relaxed or no convexity assumptions

DOI10.1142/S0219199717500092zbMath1376.35049arXiv1603.08559OpenAlexW2962772152MaRDI QIDQ5370485

Nicolai V. Krylov

Publication date: 20 October 2017

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1603.08559

zbMATH Keywords

fully nonlinear elliptic equationssmooth domains

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Second-order elliptic systems (35J47)

Related Items

The Dirichlet problem for fully nonlinear elliptic equations on Riemannian manifolds, Sharp Hessian estimates for fully nonlinear elliptic equations under relaxed convexity assumptions, oblique boundary conditions and applications, High-order estimates for fully nonlinear equations under weak concavity assumptions, Hessian estimates for fully nonlinear equations via the large-\(M\)-inequality principle, The obstacle problem for a class of degenerate fully nonlinear operators, Convex semigroups on \(L^p\)-like spaces, On the inverse source identification problem in \(L^{\infty}\) for fully nonlinear elliptic PDE, An asymptotic treatment for non-convex fully nonlinear elliptic equations: Global Sobolev and BMO type estimates, Regularity theory for \(L^n\)-viscosity solutions to fully nonlinear elliptic equations with asymptotical approximate convexity, Existence of solutions to a fully nonlinear free transmission problem

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the existence of smooth solutions for fully nonlinear elliptic equations with measurable ``coefficients without convexity assumptions
• On \(C^{1+\alpha}\) regularity of solutions of Isaacs parabolic equations with VMO coefficients
• To the theory of viscosity solutions for uniformly elliptic Isaacs equations
• Approximating the value functions for stochastic differential games with the ones having bounded second derivatives
• Interior a priori estimates for solutions of fully nonlinear equations
• On the rate of convergence of difference approximations for uniformly nondegenerate elliptic Bellman's equations
• To the theory of viscosity solutions for uniformly parabolic Isaacs equations
• \(W^{2,p}\)- and \(W^{1,p}\)-estimates at the boundary for solutions of fully nonlinear, uniformly elliptic equations
• Uniqueness and existence of maximal and minimal solutions of fully nonlinear elliptic PDE
• On a representation of fully nonlinear elliptic operators in terms of pure second order derivatives and its applications
• On the Existence of Solutions for Fully Nonlinear Elliptic Equations Under Relaxed Convexity Assumptions
• On fully nonlinear elliptic and parabolic equations with VMO coefficients in domains
• On the regularity theory of fully nonlinear parabolic equations: I
• Discrete Methods for Fully Nonlinear Elliptic Equations
• L^p- Theory for fully nonlinear uniformly parabolic equations
• An Ersatz Existence Theorem for Fully Nonlinear Parabolic Equations without Convexity Assumptions