On the regularity of the solutions of boundary-value problem for quasilinear elliptic systems with quadratic nonlinearity

DOI10.1007/BF02362383zbMath0866.35024MaRDI QIDQ676787

Arina A. Arkhipova Arkhipova

Publication date: 23 March 1997

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

zbMATH Keywords

quasilinear elliptic systempartial regularity up to the boundaryquadratic gradient nonlinearity

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Nonlinear boundary value problems for linear elliptic equations (35J65)

Related Items

On the regularity of solutions of model nonlinear elliptic systems with the oblique derivative type boundary condition ⋮ The monotonicity condition and a priori estimates of the Hölder norm for a class of nondiagonal elliptic systems with quadratic nonlinearity ⋮ Boundary regularity for elliptic systems under a natural growth condition ⋮ Boundary regularity for quasilinear elliptic systems with super quadratic controllable growth condition ⋮ Local regularity of weak solutions to quasilinear elliptic systems with one-sided condition on quadratic nonlinearity in the gradient ⋮ A problem with an obstacle that goes out to the boundary of the domain for a class of quadratic functionals on $\mathbb{R}^{N}$ ⋮ Variational problem with an obstacle in \(\mathbb R^N\) for a class of quadratic functionals ⋮ Problems in mathematical physics and function theory. Transl. from the Russian ⋮ Global solvability of the Cauchy-Dirichlet problem for nondiagonal parabolic systems with variational structure in the case of two spatial variables ⋮ New a priori estimates for \(q\)-nonlinear elliptic systems with strong nonlinearities in the gradient, \(1< q< 2\) ⋮ On a partial regularity up to the boundary of weak solutions to quasilinear parabolic systems with quadratic growth

Cites Work

• On a maximum principle for elliptic systems with constant coefficients
• A counter-example to the boundary regularity of solutions to elliptic quasilinear systems
• Nonlinear elliptic systems with quadratic growth
• Regularity results for quasilinear elliptic systems with nonlinear boundary conditions
• Equazioni ellittiche del II\(^ \circ\) ordine e spazi \({\mathcal L}^{(2,\lambda)}\)
• Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105)
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item