Related papers: On some partial data Calder\'on type problems with…
We prove local boundedness of generalized solutions to a large class of variational problems of linear growth including boundary value problems of minimal surface type and models from image analysis related to the procedure of…
We present explicit formulas for solutions to nonhomogeneous boundary value problems involving any positive power of the Laplacian in the half-space. For non-integer powers the operator becomes nonlocal and this requires a suitable…
In this article the correctness of al inear inverse problem with semi-nonlocal boundary conditions for a three-dimensional equation in a parallelepiped is considered. The equation itself is a fourth order mixed type equation of the second…
We study the presence of a non-trivial revival effect in the solution of linear dispersive boundary value problems for two benchmark models which arise in applications: the Airy equation and the dislocated Laplacian Schr{\"o}dinger…
We prove the existence and $C^{1,\alpha}$ regularity of solutions to nonlocal fully nonlinear elliptic equations with gradient constraints. We do not assume any regularity about the constraints; so the constraints need not be $C^1$ or…
We study elliptic equations of order $2m$ with nonlocal boundary-value conditions in plane angles and in bounded domains, dealing with the case where the support of nonlocal terms intersects the boundary. We establish necessary and…
In this paper we prove the existence of weak solutions to degenerate parabolic systems arising from the fully coupled moisture movement, solute transport of dissolved species and heat transfer through porous materials. Physically relevant…
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…
We consider boundary element methods where the Calder\'on projector is used for the system matrix and boundary conditions are weakly imposed using a particular variational boundary operator designed using techniques from augmented…
We establish the existence of weak solutions of a nonlinear radiation-type boundary value problem for elliptic equation on divergence form with discontinuous leading coefficient. Quantitative estimates play a crucial role on the real…
The purpose of this article is to study extrapolation of solvability for boundary value problems of elliptic systems in divergence form on the upper half-space assuming De Giorgi type conditions. We develop a method allowing to treat each…
In this paper we study elliptic partial differential equations with rapidly varying diffusion coefficient that can be represented as a perturbation of a reference coefficient. We develop a numerical method for efficiently solving multiple…
A wide variety of (fixed-point) iterative methods for the solution of nonlinear equations (in Hilbert spaces) exists. In many cases, such schemes can be interpreted as iterative local linearization methods, which, as will be shown, can be…
The problem of interest in this article is to study the (nonlocal) inverse problem of recovering a potential based on the boundary measurement associated with the fractional Schr\"{o}dinger equation. Let $0<a<1$, and $u$ solves…
This paper deals with an initial and boundary value problem for a system coupling equation and boundary condition both of Cahn-Hilliard type; an additional convective term with a forced velocity field, which could act as a control on the…
We provide symmetrization results in the form of mass concentration comparisons for fractional singular elliptic equations in bounded domains, coupled with homogeneous external Dirichlet conditions. Two types of comparison results are…
Two problems incorporating a set of horizontal linear potentials crossed by a sloped linear potential are analytically solved and compared with numerical results: (a) the case where boundary conditions are specified at the ends of a finite…
We study a degenerate elliptic equation, proving existence results of distributional solutions in some borderline cases.
Concerned with elliptic operators with stationary random coefficients governed by linear or nonlinear mixing conditions and bounded (or unbounded) $C^1$ domains, this paper mainly studies (weighted) annealed Calder\'on-Zygmund estimates,…
We prove the natural weighted Calder\'{o}n and Zygmund estimates for solutions to elliptic and parabolic obstacle problems in nondivergence form with discontinuous coefficients and irregular obstacles. We also obtain Morrey regularity…