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We study boundary gradient estimates for second-order divergence type parabolic and elliptic systems in $C^{1,alpha}$ domains. The coefficients and data are assumed to be Holder in the time variable and all but one spatial variables. This type of systems arises from the problems of linearly elastic laminates and composite materials.
For a general class of divergence type quasi-linear degenerate parabolic equations with differentiable structure and lower order coefficients form bounded with respect to the Laplacian we obtain $L^q$-estimates for the gradients of solutions, and for
We consider parabolic systems with nonlinear dynamic boundary conditions, for which we give a rigorous derivation. Then, we give them several physical interpretations which includes an interpretation for the porous-medium equation, and for certain re
This paper studies the Sobolev regularity estimates of weak solutions of a class of singular quasi-linear elliptic problems of the form $u_t - mbox{div}[mathbb{A}(x,t,u, abla u)]= mbox{div}[{mathbf F}]$ with homogeneous Dirichlet boundary conditions
We discuss counterexamples to the validity of the weak Maximum Principle for linear elliptic systems with zero and first order couplings and prove, through a suitable reduction to a nonlinear scalar equation, a quite general result showing that some
This paper is focused on the local interior $W^{1,infty}$-regularity for weak solutions of degenerate elliptic equations of the form $text{div}[mathbf{a}(x,u, abla u)] +b(x, u, abla u) =0$, which include those of $p$-Laplacian type. We derive an ex