The C1,1—character of solutions of second order elliptic equations with gradient constraint

DOI10.1080/03605308108820181zbMath0458.35035OpenAlexW1984354017MaRDI QIDQ3907904

Michael Wiegner

Publication date: 1981

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605308108820181

zbMATH Keywords

elliptic equationlocal estimategradient constraintstochastic control problemselastic-plastic torsion problemLipschitz continuity of the gradient

Mathematics Subject Classification ID

Control/observation systems governed by partial differential equations (93C20) Smoothness and regularity of solutions to PDEs (35B65) Nonlinear elasticity (74B20) Nonlinear elliptic equations (35J60)

Related Items (21)

One-sided problems for elliptic operators with convex constraints on the gradient of the solution. II ⋮ Regularity theorem for a one-sided problem with convex constraints on the gradient of the solution ⋮ On the rate of convergence of solutions in free boundary problems via penalization ⋮ On the solutions of the problem for a singular ergodic control ⋮ On an axially symmetric elastic-plastic torsion problem ⋮ Elliptic gradient constraint problem ⋮ An overview of unconstrained free boundary problems ⋮ The regularity of some vector-valued variational inequalities with gradient constraints ⋮ Nonlocal equations with gradient constraints ⋮ Double obstacle problems and fully nonlinear PDE with non-strictly convex gradient constraints ⋮ The Eigenvalue Problem of Singular Ergodic Control ⋮ Global optimal regularity for variational problems with nonsmooth non-strictly convex gradient constraints ⋮ Lagrange multipliers and non-constant gradient constrained problem ⋮ An eigenvalue problem for a fully nonlinear elliptic equation with gradient constraint ⋮ Boundary regulatity and uniqueness for an elliptic equations with gradient constraint ⋮ Non-convex Hamilton-Jacobi equations with gradient constraints ⋮ A free boundary problem arising in PDE optimization ⋮ Unnamed Item ⋮ A semi-smooth Newton method for solving elliptic equations with gradient constraints ⋮ HJB Equations with Gradient Constraint Associated with Controlled Jump-Diffusion Processes ⋮ One-sided problems for elliptic operators with convex constraints on the gradient of the solution. I

Cites Work

• The Lipschitz character of the stress tensor, when twisting an elastic plastic bar
• A second order elliptic equation with gradient constraint

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