Related papers: Remarks on the maximal regularity for parabolic bo…
In this note we consider the initial boundary value problem for the heat equation on cylinders based on Lipschitz domains with Besov data. We obtain a regularity exponent for the solution that improves the rate of convergence of nonlinear…
End-point maximal $L^1$-regularity for parabolic initial-boundary value problems is considered. For the inhomogeneous Dirichlet and Neumann data, maximal $L^1$-regularity for initial-boundary value problems is established in time end-point…
The primary objective of this work is to establish pointwise gradient estimates for solutions to a class of parabolic nonlinear nonlocal measure data problems, expressed in terms of caloric Riesz potentials of the data. As a consequence of…
This paper is dedicated to the proof of new maximal regularity results involving Besov spaces for the heat equation in the half-space or in bounded or exterior domains of R^n. We strive for time independent a priori estimates in regularity…
We prove some sharp regularity results for solutions of classical first order hyperbolic initial boundary value problems. Our two main improvements on the existing litterature are weaker regularity assumptions for the boundary data and…
The author extends previous results to general classes of equations under weaker assumptions obtained in 2016 by Bao, Dong and Jiao concerning the study of the regularity of solutions for the first initial-boundary value problem for…
In this paper we establish weighted $L^{q}$-$L^{p}$-maximal regularity for linear vector-valued parabolic initial-boundary value problems with inhomogeneous boundary conditions of static type. The weights we consider are power weights in…
In the prototypical setting of non-Euclidean geometry, the 2-dimensional Real Hyperbolic space $\mathbb{H}^2$, we consider the Carleson's problem for the Schr\"odinger equation and improve the best known result until now by proving that the…
We develop an optimal regularity theory for parabolic partial differential equations in weighted mixed norm Sobolev-Zygmund spaces. The results extend the classical Schauder estimates to coefficients that are merely measurable in time and…
This paper is concerned with the regularity of solutions to parabolic evolution equations. Special attention is paid to the smoothness in the specific anisotropic scale $\ B^{r\mathbf{a}}_{\tau,\tau}, \…
A heat equation with uncertain domains is thoroughly investigated. Statistical moments of the solution is approximated by the counterparts of the shape derivative. A rigorous proof for the existence of the shape derivative is presented.…
In this paper, we derive a priori estimates for the gradient and second order derivatives of solutions to a class of Hessian type fully nonlinear parabolic equations with the first initial-boundary value problem on Riemannian manifolds.…
In this paper we prove higher regularity for 2m-th order parabolic equations with general boundary conditions. This is a kind of maximal L_p-L_q regularity with differentiability, i.e. the main theorem is isomorphism between the solution…
In this paper there are estimated the derivatives of the solution of an initial boundary value problem for a nonlinear uniformly parabolic equation in the interior with the total variation of the boundary data and the L^{infinity}-norm of…
In this note we derive large-scale regularity properties of solutions to second-order linear elliptic equations with random coefficients on the half- space with homogeneous Neumann boundary data; it is a companion to arXiv:1604.02717 in…
In this article we prove results concerning upper and lower decay estimates for homogeneous Sobolev norms of solutions to a rather general family of parabolic equations. Following the ideas of Kreiss, Hagstrom, Lorenz and Zingano, we use…
We consider the linear heat equation on a bounded domain and on an exterior domain. We study estimates of any order derivatives of the solution locally in time in the Lebesgue spaces. We give a proof of the estimates in the end-point cases…
We study second order hyperbolic equations with initial conditions, a nonhomogeneous Dirichlet boundary condition and a source term. We prove the solution possesses $H^1$ regularity on any piecewise $C^1$-smooth non-timelike hypersurfaces.…
In this work there is established an optimal existence and regularity theory for second order linear parabolic differential equations on a large class of noncompact Riemannian manifolds. Then it is shown that it provides a general unifying…
We consider the parabolic Lam\'{e} system on a bounded domain. We focus on two types of inequalities for higher-order derivatives of solutions. The first is related to an $L^p$-$L^p$ estimate locally in time in the Lebesgue space setting,…