We prove that the well-known trace theorem for weighted Sobolev spaces holds true under minimal regularity assumptions on the domain. Using this result, we prove the existence of a bounded linear righ...
We prove that an $L^{\infty }$ potential in the Schrödinger equation in three and higher dimensions can be uniquely determined from a finite number of boundary measurements, provided it belongs to a k...
We present a novel direct transcription method to solve optimization problems subject to nonlinear differential and inequality constraints. In order to provide numerical convergence guarantees, it is ...
We develop a homogenization method to tackle the problem of a diffusion process through a cracked medium. We show that the cracked surface of the domain induces a source term in the homogenized equati...
We consider the Galerkin finite element approximation of an elliptic Dirichlet boundary control model problem governed by the Laplacian operator. The analytical setting of this problem uses $L^2$ cont...
We apply Robin penalization to Dirichlet optimal control problems governed by semilinear elliptic equations. Error estimates in terms of the penalization parameter are stated. The results are compared...
We analyze a least-squares strong-form kernel collocation formulation for solving second-order elliptic PDEs on smooth, connected, and compact surfaces with bounded geometry. The methods do not requir...
To model subsurface flow in uncertain heterogeneous\ fractured media an elliptic equation with a discontinuous stochastic diffusion coefficient - also called random field - may be used. In case of a o...
This work aims to prove a Hardy-type inequality and a trace theorem for a class of function spaces on smooth domains with a nonlocal character. Functions in these spaces are allowed to be as rough as ...
This paper presents adaptive boundary element methods for positive, negative, as well as zero order operator equations, together with proofs that they converge at certain rates. The convergence rates ...
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This chapter gives an expository introduction to the Galerkin-BEM for the elliptic boundary value problems from the mathematical point of view. Emphasis will be placed on the variational formulations ...
The purpose of this paper is to prove existence and uniqueness in Sobolev or Holder spaces for a transmission problem which describes the flow of a viscous incompressible fluid past a porous particle ...
The purpose of this note is to prove a version of the Trace Theorem for domains which are locally subgraph of a Holder continuous function. More precisely, let $\eta\in C^{0,\alpha}(\omega)$, $0<\alp...
The fractional Laplacian in R^d has multiple equivalent characterizations. Moreover, in bounded domains, boundary conditions must be incorporated in these characterizations in mathematically distinct ...
The coupled Darcy-Stokes problem is widely used for modeling fluid transport in physical systems consisting of a porous part and a free part. In this work we consider preconditioners for monolitic sol...
The Richards' equation is a model for flow of water in unsaturated soils. The coefficients of this (nonlinear) partial differential equation describe the permeability of the medium. Insufficient or un...
Subsurface flows are commonly modeled by advection-diffusion equations. Insufficient measurements or uncertain material procurement may be accounted for by random coefficients. To represent, for examp...
Spectral boundary-value problems with discrete spectrum are considered for second-order strongly elliptic systems of partial differential equations in a domain whose boundary is compact and may be , ,...
Piezoelectric appliances have become hugely important in the past century and computer simulations play an essential part in the modern design process thereof. While much work has been invested into t...