Local regularity of weak solutions to quasilinear elliptic systems with one-sided condition on quadratic nonlinearity in the gradient

DOI10.1007/S10958-021-05380-9zbMath1465.35085OpenAlexW3163051850MaRDI QIDQ2027455

Arina A. Arkhipova Arkhipova

Publication date: 27 May 2021

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-021-05380-9

zbMATH Keywords

local smoothnessnondiagonal principal matrixquadratic nonlinearity in the gradient

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Weak solutions to PDEs (35D30) Quasilinear elliptic equations (35J62) Boundary value problems for second-order elliptic systems (35J57)

Related Items (4)

Parabolic systems with quadratic nonlinearities in the gradient. Regularity of solutions ⋮ Unbounded weak solutions to strongly \(q\)-nonlinear elliptic systems. Local regularity ⋮ Local regularity of weak solutions to a class of parabolic systems with quadratic nonlinearities in the gradient ⋮ Regularity conditions for nonlinear elliptic systems with quadratic nonlinearities in the gradient

Cites Work

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• On two-dimensional quasi-linear elliptic systems
• The monotonicity condition and a priori estimates of the Hölder norm for a class of nondiagonal elliptic systems with quadratic nonlinearity
• On the regularity of the solutions of boundary-value problem for quasilinear elliptic systems with quadratic nonlinearity
• Partial regularity of solutions to model Venttsel problem for quasilinear elliptic systems of equations with quadratic nonlinearity relative to the gradient
• Existence and partial regularity results for the heat flow for harmonic maps
• Some regularity results for quasilinear elliptic systems of second order
• Nonlinear elliptic systems with quadratic growth
• On quasilinear elliptic systems of diagonal form
• A new partial regularity proof for solutions of nonlinear elliptic systems
• Partial regularity up to the boundary for weak solutions of elliptic systems with nonlinearity \(q\) greater than two
• Global solvability of the Cauchy-Dirichlet problem for nondiagonal parabolic systems with variational structure in the case of two spatial variables
• Global solvability of the Cauchy-Dirichlet problem for the class of nondiagonal parabolic systems with \(q\)-nonlinearity in the gradient, \(1< q< 2\)
• Global solvability of the Cauchy-Dirichlet problem for a class of strongly nonlinear parabolic systems
• Linear and quasilinear elliptic equations
• New a priori estimates for \(q\)-nonlinear elliptic systems with strong nonlinearities in the gradient, \(1< q< 2\)
• Solvability problem for nondiagonal elliptic systems with a quadratic nonlinearity in the gradient (the two-dimensional case)
• Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105)
• On the existence of weak solutions of perturbated systems with critical growth.

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