Related papers: Boundary value problems of elliptic operators and …
We discuss finite difference techniques for hyperbolic equations in non-trivial domains, as those that arise when simulating black hole spacetimes. In particular, we construct dissipative and difference operators that satisfy the {\it…
A new boundary value problem for partial differential equations is discussed. We consider an arbitrary solution of an elliptic or parabolic equation in a given domain and no boundary conditions are assumed. We study which restrictions the…
To empower the mathematical hitchhiker wishing to use operator methods in geometry and topology, we present this user's guide to first-order elliptic boundary value problems. Existence, regularity, and Fredholmness are discussed for general…
Parameter--elliptic pseudodifferential operators given on a closed smooth manifold are investigated on the extended Sobolev scale. This scale consists of all Hilbert spaces that are interpolation spaces with respect to the Hilbert Sobolev…
The main purpose of this paper is to address some questions concerning boundary value problems related to the Laplacian and bi-Laplacian operators, set in the framework of classical $H^s$ Sobolev spaces on a bounded Lipschitz domain of R^N.…
In this work we propose a novel approach to investigate boundary value problems (BVPs) for fully third order differential equations. It is based on the reduction of BVPs to operator equations for the nonlinear terms but not for the…
We study families of strongly elliptic, second order differential operators with singular coefficients on domains with conical points. We obtain uniform estimates on their inverses and on the regularity of the solutions to the associated…
We study the boundary integral operator induced from the fractional Laplace equation in a bounded smooth domain. For $1/2 < \alpha? < 1$, we show the bijectivity of the boundary integral operator $S_{2\alpha} : L^p(\partial \Omega)…
In a refined Sobolev scale, we investigate an elliptic boundary-value problem with additional unknown functions in boundary conditions for which the maximum of orders of boundary operators is grater than or equal to the order of the…
We investigate elliptic boundary-value problems with additional unknown functions on the boundary of a Euclidean domain. These problems were introduced by Lawruk. We prove that the operator corresponding to such a problem is bounded and…
We investigate elliptic boundary-value problems with additional unknown functions in boundary conditions. These problems were introduced by Lawruk. We prove that the operator corresponding to such a problem is bounded and Fredholm on…
In the paper we consider the theory of elliptic operators acting in subspaces defined by pseudodifferential projections. This theory on closed manifolds is connected with the theory of boundary value problems for operators violating…
We develop a functional model for operators arising in the study of boundary-value problems of materials science and mathematical physics. We then provide explicit formulae for the resolvents of the associated extensions of symmetric…
In this paper we study the shape differentiability properties of a class of boundary integral operators and of potentials with weakly singular pseudo-homogeneous kernels acting between classical Sobolev spaces, with respect to smooth…
In this paper operator pencils $A(x,D,\lambda)$ are studied which act on a manifold with boundary and satisfy the condition of $N$-ellipticity with parameter, a generalization of the notion of ellipticity with parameter as introduced by…
We show that elliptic complexes of (pseudo)differential operators on smooth compact manifolds with boundary can always be complemented to a Fredholm problem by boundary conditions involving global pseudodifferential projections on the…
We prove sparse bounds for pseudodifferential operators associated to H\"ormander symbol classes. Our sparse bounds are sharp up to the endpoint and rely on a single scale analysis. As a consequence, we deduce a range of weighted estimates…
The purpose of this paper is to establish the theory of stochastic pseudo-differential operators and give its applications in stochastic partial differential equations. First, we introduce some concepts on stochastic pseudo-differential…
In the first part of the article, we give necessary and sufficient conditions for the solvability of a class of nonlinear elliptic boundary value problems with nonlinear boundary conditions involving the q-Laplace-Beltrami operator. In the…
We consider a boundary value problem in a bounded domain involving a degenerate operator of the form $$L(u)=-\textrm{div} (a(x)\nabla u)$$ and a suitable nonlinearity $f$. The function $a$ vanishes on smooth 1-codimensional submanifolds of…