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Given a Riemannian manifold (M, g), we study the solutions of heat equations associated with second order differential operators in divergence form that are uniformly elliptic with respect to g . Ty...
This paper introduces the hierarchical interpolative factorization for integral equations (HIF-IE) associated with elliptic problems in two and three dimensions.This factorization takes the form of an...
This paper introduces the hierarchical interpolative factorization for elliptic partial differential equations (HIF-DE) in two (2D) and three dimensions (3D). This factorization takes the form of an a...
The notion of quasi boundary triples and their Weyl functions is an abstract concept to treat spectral and boundary value problems for elliptic partial differential equations.
We prove sharp stability estimates for the variation of the eigenvalues of non-negative self-adjoint elliptic operators of arbitrary even order upon variation of the open sets on which they are define...
We consider a second-order selfadjoint elliptic operator with an anisotropic di usion matrix having a jump across a smooth hypersurface. We prove the existence of a weight-function such that a Carlema...
In this paper we prove that, under suitable assumptions on > 0, the operator L = (1+|x| ) admits realizations generating contraction or analytic semigroups in Lp(RN). For some values of , we also ...
Let be an open subset of Rd with 0 ∈ . Further let H = −Pd i,j=1 @i cij @j be a second-order partial differential operator with domain C∞ c ( ) where the coefficients cij ∈ W1,∞ loc ( ) are re...

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