Related papers: The Perron solution for vector-valued equations
We study the boundary value problem with Radon measures for nonnegative solutions of $L_Vu:=-\Delta u+Vu=0$ in a bounded smooth domain $\Gw$, when $V$ is a locally bounded nonnegative function. Introducing some specific capacity, we give…
In this note we discuss an abstract framework for standard boundary value problems in divergence form with maximal monotone relations as "coefficients". A reformulation of the respective problems is constructed such that they turn out to be…
In this note we study the Dirichlet problem associated with a version of prime end boundary of a bounded domain in a complete metric measure space equipped with a doubling measure supporting a Poincare inequality. We show the resolutivity…
We consider a boundary value problem for the parabolic Lam\'e type operator being a linearization of the Navier-Stokes' equations for compressible flow of Newtonian fluids. It consists of recovering a vector-function, satisfying the…
This paper systematically studies Hilbert boundary value problems for hyper monogenic functions on the hyperplane for the solutions being of any integer orders at the infinity, where the negative order cases are new even when restricted to…
This paper is concerned with existence of viscosity solutions of non-translation invariant nonlocal fully nonlinear equations. We construct a discontinuous viscosity solution of such nonlocal equation by Perron's method. If the equation is…
In this work we obtain sufficient conditions for the existence of bounded solutions of a resonant multi-point second-order boundary value problem, with a fully differential equation. The noninvertibility of the linear part is overcome by a…
Take a set of balls in $\mathbb R^d$. We find a subset of pairwise disjoint balls whose combined perimeter controls the perimeter of the union of the original balls. This can be seen as a boundary version of the Vitali covering lemma. We…
We investigate solvability of a continuous Dirichlet boundary value problem together with its classical discretization using a gobal diffeomorphism theorem.
We present an explicit solution of the $A_r$ $T$-system for arbitrary boundary conditions. For each boundary, this is done by constructing a network, i.e. a graph with positively weighted edges, and the solution is expressed as the…
The discussion of our recent work concerning the vector solution of boundary-value problems in electromagnetism is extended to the case of no azimuthal symmetry by means of the spin-weighted spherical harmonics.
The vector transform operators are investigated; these operators are used at the solution of boundary value problems in piecewise homogeneous spherically symmetric areas. In particular, examples of transformation operators for vector…
Motivated by the study of systems of higher order boundary value problems with functional boundary conditions, we discuss, by topological methods, the solvability of a fairly general class of systems of perturbed Hammerstein integral…
Bounded variation estimates of Galerkin approximations are established in order to extract an almost everywhere convergent subsequence of Galerkin approximations. As a result we prove existence of weak solutions of initial boundary value…
We establish a Schn$\ddot{\text{u}}$rer's convergence result and then apply it to obtain the existence of solutions on the second boundary value problem for a family of special Lagrangian equations
We consider well-posedness of the boundary value problem in presence of an inclusion with complex conductivity $k$. We first consider the transmission problem in $\mathbb{R}^d$ and characterize solvability of the problem in terms of the…
In this article we introduce a simple straightforward and powerful method involving symbolic manipulation, Picard iteration, and auxiliary variables for approximating solutions of partial differential boundary value problems. The method is…
In this paper we study the values of Markov-Davenport forms, which are specially normalized binary quadratic forms. We generalize the Perron identity for ordinary continued fractions for sails to the case of arbitrary broken lines.
We study the boundary behavior of solutions to the Dirichlet problems for integro-differential operators with order of differentiability $s \in (0, 1)$ and summability $p>1$. We establish a nonlocal counterpart of the Wiener criterion,…
We study elliptic and parabolic boundary value problems in spaces of mixed scales with mixed smoothness on the half space. The aim is to solve boundary value problems with boundary data of negative regularity and to describe the…