Related papers: Oblique Derivative Problems for Elliptic Equations…

We investigate existence and nonexistence of stationary stable nonconstant solutions, i.e. patterns, of semilinear parabolic problems in bounded domains of Riemannian manifolds satisfying Robin boundary conditions. These problems arise in…

We show that convex viscosity solutions of the Lagrangian mean curvature equation are regular if the Lagrangian phase has H\"older continuous second derivatives.

We consider the axisymmetric Navier-Stokes equations in a finite cylinder $\Omega\subset\mathbb{R}^3$. We assume that $v_r$, $v_\varphi$, $\omega_\varphi$ vanish on the lateral boundary $\partial \Omega$ of the cylinder, and that $v_z$,…

We examine the conditional regularity of the solutions of Navier-Stokes equations in the entire three-dimensional space under the assumption that the data are axially symmetric. We show that if positive part of the radial component of…

We establish the existence and uniqueness of solutions of fully nonlinear elliptic second-order equations like $H(v,Dv,D^{2}v,x)=0$ in smooth domains without requiring $H$ to be convex or concave with respect to the second-order…

This paper concerns fully nonlinear elliptic obstacle problems with oblique boundary conditions. We investigate the existence, uniqueness and $W^{2,p}$-regularity results by finding approximate non-obstacle problems with the same oblique…

We consider one-dimensional inhomogeneous parabolic equations with higher-order elliptic differential operators subject to periodic boundary conditions. In our main result we show that the property of continuous maximal regularity is…

In this paper, we study the boundary H\"older regularity for solutions to the fractional Dirichlet problem in unbounded domains with boundary \begin{equation*} \begin{cases} (-\Delta)^s u(x) = g(x),&\text{in } \Omega, u(x)=0, &\text{in }…

We study a new formulation for the eikonal equation |grad u| =1 on a bounded subset of R^2. Considering a field P of orthogonal projections onto 1-dimensional subspaces, with divergence bounded in L^2, we prove existence and uniqueness for…

We show that bounded solutions of the quasilinear elliptic equation $\Delta_{p(x)} u=g+div(\textbf{F})$ are locally H\"{o}lder continuous provided that the functions $g$ and $\textbf{F}$ are in suitable Lebesgue spaces.

In this paper, the continuity of solutions for elliptic equations in divergence form with distributional coefficients is considered. Inspired by the discussion on necessary and sufficient conditions for the form boundedness of elliptic…

This paper considers a class of nonlinear, degenerate drift- diffusion equations. We study well-posedness and regularity properties of the solutions, with the goal to achieve uniform H\"{o}lder regularity in terms of $L^p$-bound on the…

We prove sharp boundary H{\"o}lder regularity for solutions to equations involving stable integro-differential operators in bounded open sets satisfying the exterior $C^{1,\text{dini}}$-property. This result is new even for the fractional…

Let $2\le n\le 5$. We establish an apriori interior H\"older regularity of $C^2$-stable solutions to the semilinear equation $-\Delta u=f(u)$ in any domain of $R^n$ for any nonlinearity $f\in C^{0,1}(R) $.If $f $ is nondecreasing and convex…

We prove Holder regularity for solutions of non divergence integro-differential equations with non necessarily even kernels. The even/odd decomposition of the kernel can be understood as a sum of a diffusion and a drift term. In our case we…

We establish partial regularity result for vector-valued solutions to second order elliptic system in divergence form. The coefficients safisfies Dini condition respect to $(x,u)$ with growth order lager than 2. We prove $C^1$-regularity of…

In this paper, we study the boundary pointwise regularity for the divergence form elliptic boundary problem on domains with rough boundaries, specifically uniform domains. In general, it is not straightforward to define weak solutions for…

We revisit the classical theory of linear second-order uniformly elliptic equations in divergence form whose solutions have H\"older continuous gradients, and prove versions of the generalized maximum principle, the $C^{1,\alpha}$-estimate,…

We consider an elliptic polyharmonic problem of any order which takes place in a punctured bounded domain with Navier conditions. We prove that if the domain is convex in one direction and symmetric with respect to the reflections induced…

In this paper, a geometric condition on domains will be given which guarantees the boundary differentiability of solutions of elliptic equations, that is, the solutions are differentiable at any boundary point. We will show that this…