Related papers: Generalizations of the Dirichlet problem for biana…

In the paper the Dirichlet problem with non-classical conditions not requiring agreement conditions is considered for a fourth order pseudoparabolic equation with non-classical coefficients. The equivalence of these conditions with the…

We solve the Dirichlet problem for $k$-Hessian equations on compact complex manifolds with boundary, given the existence of a subsolution. Our method is based on a second order a priori estimate of the solution on the boundary with a…

We start by presenting a generalization of a discrete wave equation that is particularly satisfied by the entries of the matrix coefficients of the refinement equation corresponding to the multiresolution analysis of Alpert. The entries are…

In this work, we introduce the notion of regularization of bifunctions in a similar way as the well- known convex, quasiconvex and lower semicontinuous regularizations due to Crouzeix. We show that the Equilibrium Problems associated to…

We study whether the solutions of a parabolic equation with diffusion given by the fractional Laplacian and a dominating gradient term satisfy Dirichlet boundary data in the classical sense or in the generalized sense of viscosity…

The main result of the paper is an extension of the Dirichlet problem from (closures of) bounded open domains U to arbitrary compact subsets X of the complex plane, i.e. the closure of the corresponding space of functions which are harmonic…

We study second-order stochastic parabolic equations in a cylindrical domain with homogeneous Dirichlet boundary conditions. Under a natural compatibility condition on the gradient-type noise, we establish global Schauder estimates in…

We prove some conditions on the existence of natural boundaries of Dirichlet series. We show that generically the presumed boundary is the natural one. We also give an application of natural boundaries in determining asymptotic results.

We provide a new result on the existence of extremal solutions for second-order Dirichlet problems with deviation argument. As a novelty in this work, the nonlinearity need not be continuous or monotone. In order to obtain this new result,…

We consider the Dirichlet problem for a class of elliptic and parabolic equations in the upper-half space $\mathbb{R}^d_+$, where the coefficients are the product of $x_d^\alpha, \alpha \in (-\infty, 1),$ and a bounded uniformly elliptic…

Let $L$ be an infinitely degenerate second-order linear operator defined on a bounded smooth Euclidean domain. Under weaker conditions than those of H\"ormander, we show that the Dirichlet problem associated with $L$ has a unique smooth…

We investigate the Dirichlet solution for a semianalytic continuous function on the boundary of a semianalytic bounded domain in the plane. We show that the germ of the Dirichlet solution at a boundary point with angle greater than 0 lies…

In this paper we use a natural iteration technique to prove existence of solutions to nonlinear Dirichlet problems. Among the examples included is the prescribed mean curvature equation. The nature of the technique allows applications to…

In this work, we consider the Dirichlet boundary value problem for nonlinear triharmonic equation. Due to the reduction of the nonlinear boundary value problem to operator equation for the nonlinear term and the unknown second normal…

The present paper establishes a certain duality between the Dirichlet and Regularity problems for elliptic operators with $t$-independent complex bounded measurable coefficients ($t$ being the transversal direction to the boundary). To be…

We consider the linear second order PDO's $$ \mathscr{L} = \mathscr{L}_0 - \partial_t : = \sum_{i,j =1}^N \partial_{x_i}(a_{i,j} \partial_{x_j} ) - \sum_{j=i}^N b_j \partial_{x_j} - \partial _t,$$and assume that $\mathscr{L}_0$ has…

We settle the issue of well-posedness for the Dirichlet problem for a higher order elliptic system ${\mathcal L}(x,D_x)$ with complex-valued, bounded, measurable coefficients in a Lipschitz domain $\Omega$, with boundary data in Besov…

We study a Dirichlet problem in the entire space for some nonlocal degenerate elliptic operators with internal nonlinearities. With very mild assumptions on the boundary datum, we prove existence and uniqueness of the solution in the…

We consider the Poisson equation with homogeneous Dirichlet conditions in a family of domains in $R^{n}$ indexed by a small parameter $\epsilon$. The domains depend on $\epsilon$ only within a ball of radius proportional to $\epsilon$ and,…

In this paper we prove that any solution of the $m$-polyharmonic Poisson equation in a Reifenberg-flat domain with homogeneous Dirichlet boundary condition, is $\mathscr{C}^{m-1,\alpha}$ regular up to the boundary. To achieve this result we…