Global \(L^{\infty }\) gradient estimates for solutions to a certain degenerate elliptic equation

DOI10.1016/j.na.2010.09.006zbMath1202.35103OpenAlexW2019999510MaRDI QIDQ608406

Lorenzo Brasco

Publication date: 25 November 2010

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

Full work available at URL: https://doi.org/10.1016/j.na.2010.09.006

zbMATH Keywords

Neumann boundary value problemdegenerate elliptic equationstraffic congestionnon-convex variational problems

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Smoothness and regularity of solutions to PDEs (35B65) Nonlinear elliptic equations (35J60) Degenerate elliptic equations (35J70)

Related Items (18)

Pointwise bounds for minimizers of some anisotropic functionals ⋮ On the Lipschitz character of orthotropic \(p\)-harmonic functions ⋮ Global Lipschitz continuity for minima of degenerate problems ⋮ On a degenerate problem in the calculus of variations ⋮ Regularity results for vectorial minimizers of a class of degenerate convex integrals ⋮ Regularity results for very degenerate elliptic equations ⋮ Higher regularity for weak solutions to degenerate parabolic problems ⋮ Symmetry of minimizers with a level surface parallel to the boundary ⋮ Fractional Sobolev regularity for solutions to a strongly degenerate parabolic equation ⋮ Higher regularity for minimizers of very degenerate convex integrals ⋮ Higher regularity in congested traffic dynamics ⋮ An excess-decay result for a class of degenerate elliptic equations ⋮ A weak comparison principle for solutions of very degenerate elliptic equations ⋮ Besov regularity for a class of singular or degenerate elliptic equations ⋮ Very degenerate elliptic equations under almost critical Sobolev regularity ⋮ On the regularity of solutions to a class of degenerate PDE's with lower order terms ⋮ A Viscosity Equation for Minimizers of a Class of Very Degenerate Elliptic Functionals ⋮ Higher regularity for minimizers of very degenerate integral functionals

Cites Work

• Continuity in two dimensions for a very degenerate elliptic equation
• Ordinary differential equations, transport theory and Sobolev spaces
• Linear and quasilinear elliptic equations
• The L\(^p\)-integrability of the partial derivatives of a quasiconformal mapping
• C1 + α local regularity of weak solutions of degenerate elliptic equations
• Nonlinear elliptic systems with certain unbounded coefficients
• Boundary regularity for solutions of degenerate elliptic equations
• An existence result for a nonconvex variational problem via regularity
• Local Stress Regularity in Scalar Nonconvex Variational Problems
• On the Lipschitz regularity for certain elliptic problems
• A Continuous Model of Transportation
• Congested traffic dynamics, weak flows and very degenerate elliptic equations
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