Related papers: Gradient higher integrability for degenerate parab…
We study the construction and convergence of decoupling multistep schemes of higher order using the backward differentiation formulae for an elliptic-parabolic problem, which includes multiple-network poroelasticity as a special case. These…
In this paper, we establish the existence of solutions for a particular class of degenerate hyperbolic equations. Following this, we approximate these degenerate equations by employing a sequence of uniformly hyperbolic equations. Notably,…
We prove locally in time the existence of a smooth solution for multidimensional two-phase Stefan problem for degenerate parabolic equations of the porous medium type. We establish also natural H\"{o}lder class for the boundary conditions…
We establish the pointwise continuity of bounded weak solutions to of a class of scalar parabolic equations and strongly coupled parabolic systems. Our approach to the regularity theory of parabolic scalar equations is quite elementary and…
This paper discusses parabolic reverse H\"older inequalities and their connections to parabolic Muckenhoupt weights. The main result gives several characterizations for this class of weights. There are challenging features related to the…
We prove the H\"older continuity for weak solutions to parabolic p-Laplace equations on the Heisenberg group. We deduce this result while considering an optimal tail condition.
We establish regularity results for viscosity solutions to a class of quasilinear parabolic equations exhibiting nonhomogeneous degeneracy or singularity (a double phase regime) of the form \[ u_t - \big(|Du|^{\mathfrak{p}} +…
We prove that $L^2$ weak solutions to hypoelliptic equations with bounded measurable coefficients are H\"older continuous. The proof relies on classical techniques developed by De Giorgi and Moser together with the averaging lemma and…
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…
We present a local almost everywhere regularity result for a general nonlinear non-diagonal parabolic system, which main part depends on symmetric part of the gradient.
The paper is a comprehensive study of the $L_p$ and the Schauder estimates for higher-order divergence type parabolic systems with discontinuous coefficients in the half space and cylindrical domains with conormal derivative boundary…
We prove global existence of a nonnegative weak solution to a degenerate parabolic system, which models the spreading of insoluble surfactant on a thin liquid film.
We establish Zaremba problem for Laplacian and $p$-Laplacian with degenerate weights when the Dirichlet condition is only imposed in a set of positive weighted capacity. We prove weighted Sobolev-Poincar\'{e} inequality with sharp…
This paper addresses the stability of a class of parabolic equations in non-cylindrical domains. We investigate the $L^\infty$-stability of systems for both nondegenerate and degenerate cases. Unlike in cylindrical domains, solutions to…
In this paper, we establish two Carleman estimates for a stochastic degenerate parabolic equation. The first one is for the backward stochastic degenerate parabolic equation with singular weight function. Combining this Carleman estimate…
In this paper we study higher order weakly hyperbolic equations with time dependent non-regular coefficients. The non-regularity here means less than H\"older, namely bounded coefficients. As for second order equations in \cite{GR:14} we…
The aim of this work is to establish numerous interrelated gradient estimates in the nonlinear nonlocal setting. First of all, we prove that weak solutions to a class of homogeneous nonlinear nonlocal equations of possibly arbitrarily low…
Functional bilevel methods estimate a lower-level function and plug it into a hypergradient, but this plug-in gradient can retain first-order bias when the lower-level problem is learned nonparametrically. To remove this bias, we develop a…
By borrowing ideas from the parabolic theory, we use a combination of De Giorgi's and Moser's methods to give some remarks on the proof of H\"older continuity of weak solutions of elliptic equations.
In this note we consider degenerate chemotaxis systems with porous media type diffusion and a source term satisfying the Hadamard growth condition. We prove the H\"older regularity for bounded solutions to parabolic-parabolic as well as for…