Related papers: Boundary pointwise regularity for the divergence f…
In this paper we are concerned with the initial boundary value problems of linear and semi-linear parabolic equations with mixed boundary conditions on non-cylindrical domains in spatial-temporal space. We obtain the existence of a weak…
The aim of this paper is to develop the regularity theory for a weak solution to a class of quasilinear nonhomogeneous elliptic equations, whose prototype is the following mixed Dirichlet $p$-Laplace equation of type \begin{align*}…
In this paper we investigate elliptic partial differential equations on Lipschitz domains in the plane whose coefficient matrices have small (but possibly nonzero) imaginary parts and depend only on one of the two coordinates. We show that…
In the present paper we investigate the following semilinear singular elliptic problem: \begin{equation*} (\rm P)\qquad \left \{\begin{array}{l} -\Delta u = \dfrac{p(x)}{u^{\alpha}}\quad \text{in} \Omega \\ u = 0\ \text{on} \Omega,\ u>0…
The aim of this paper is to establish regularity for weak solutions to the nondiagonal quasilinear degenerate elliptic systems related to H\"{o}rmander's vector fields, where the coefficients are bounded with vanishing mean oscillation. We…
In this article, we deal with the fine boundary regularity, a weighted H\"{o}lder regularity of weak solutions to the problem involving the fractional $(p,q)$ Laplacian denoted by $(-\Delta)_{p}^{s} u + (-\Delta)_{q}^{s} u = f(x)$ in…
This paper establishes pointwise estimates up to boundary for the gradient of weak solutions to a class of very singular quasilinear elliptic equations with mixed data: \begin{cases} -\operatorname{div}(A(x,D u))=g-\operatorname{div} f…
In this paper we investigate the regularity and solvability of solutions to Dirichlet problem for fully non-linear elliptic equations with gradient terms on Hermitian manifolds, which include among others the Monge-Amp\`ere equation for…
In this paper we prove the boundedness and H\"older continuity of quasilinear elliptic problems involving variable exponents for a homogeneous Dirichlet and a nonhomogeneous Neumann boundary condition, respectively. The novelty of our work…
We prove optimal boundary regularity for bounded positive weak solutions of fast diffusion equations in smooth bounded domains. This solves a problem raised by Berryman and Holland in 1980 for these equations in the subcritical and critical…
Fractional-order elliptic problems are investigated in case of inhomogeneous Dirichlet boundary data. The boundary integral form is proposed as a suitable mathematical model. The corresponding theory is completed by sharpening the mapping…
In this paper we study on smooth bounded domains the global regularity (up to the boundary) for weak solutions to systems having $p$-structure depending only on the symmetric part of the gradient.
A sharp pointwise differential inequality for vectorial second-order partial differential operators, with Uhlenbeck structure, is offered. As a consequence, optimal second-order regularity properties of solutions to nonlinear elliptic…
In this paper, exploiting variational methods, the existence of three weak solutions for a class of elliptic equations involving a general operator in divergence form and with Dirichlet boundary condition is investigated. Several special…
The theory of boundary regularity for $p$-harmonic functions is extended to unbounded open sets in complete metric spaces with a doubling measure supporting a $p$-Poincar\'e inequality, $1<p<\infty$. The barrier classification of regular…
We consider a nonlinear version of the Yamabe problem on locally conformally flat compact manifolds with boundary. The main technique we used is to derive boundary $C^2$ estimates directly from boundary $C^0$ estimates. In particular, the…
We study the convergence of the weak solution of the porous medium equation with a type of Robin boundary conditions, by tuning a parameter either to zero or to infinity. The convergence is in the strong sense, with respect to the…
The unique existence of a weak solution to the homogeneous closed Dirichlet problem on certain D-star-shaped domains is proven for a mixed elliptic-hyperbolic equation. Equations of this kind arise in models for electromagnetic wave…
This paper is concerned with boundary regularity estimates in the homogenization of elliptic equations with rapidly oscillating and high-contrast coefficients. We establish uniform nontangential-maximal-function estimates for the Dirichlet,…
We establish the regularity theory for certain critical elliptic systems with an anti-symmetric structure under inhomogeneous Neumann and Dirichlet boundary constraints. As applications, we prove full regularity and smooth estimates at the…