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UNIFORMLY ELLIPTIC OPERATORS ON RIEMANNIAN MANIFOLDS
RIEMANNIAN MANIFOLDS ELLIPTIC OPERATORS
2015/8/26
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...
Hierarchical Interpolative Factorization for Elliptic Operators:Integral Equations
Hierarchical Interpolative Factorization Elliptic Operators Integral Equations
2015/7/14
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...
Hierarchical Interpolative Factorization for Elliptic Operators:Differential Equations
Hierarchical Interpolative Factorization Elliptic Operators Differential Equations
2015/7/14
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...
Spectral estimates for resolvent differences of self-adjoint elliptic operators
Spectral estimates resolvent differences
2011/2/24
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.
Sharp spectral stability estimates via the Lebesgue measure of domains for higher order elliptic operators
Elliptic equations Dirichlet and Neumann boundary conditions stability of eigenvalues
2011/2/25
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...
Carleman estimates for elliptic operators with jumps at an interface: Anisotropic case and sharp geometric conditions
Carleman estimate elliptic operator non-smooth coecient quasimode
2011/2/21
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...
A Borg-Levinson theorem for higher order elliptic operators
A Borg-Levinson theorem elliptic operators
2010/11/15
We establish the Borg-Levinson theorem for elliptic operators of higher order with constant coefficients. The case of incomplete spectral data is also considered.
Elliptic operators with unbounded diffusion coefficients in Lp spaces
elliptic operators unbounded coefficients generation results analytic semigroups
2010/12/1
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 ...
$L_1$-uniqueness of degenerate elliptic operators
$L_1$-uniqueness degenerate elliptic operators
2010/12/13
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...
lower bound of the first eigenvalue of certain self-adjoint elliptic operators on manifolds containing long necks
lower bound manifolds containing long necks certain self-adjoint elliptic operators
2010/3/5
In this note, under certain regularity and transversality conditions we obtain a sharp lower bound of the first eigenvalue for certain self-adjoint elliptic operators on manifolds with long necks. Thi...
Strongly Elliptic Operators for a Plane Wave Diffraction Problem in Bessel Potential Spaces
Diffraction problem Strong Ellipticity Convolution type operator Wiener-Hopf operator Equivalence after extension
2008/6/26
We consider a plane wave diffraction problem by a union of several infinite strips. The problem is formulated as a boundary-transmission one for the Helmholtz equation in a Bessel potential space sett...
ON THE UNIQUE CONTINUATION PROPERTIES FOR ELLIPTIC OPERATORS WITH SINGULAR POTENTIALS
doubling property unique continuation Lipschitz domain Kato--Fefferman--Phong s potential
2007/12/11
Let $u$ be a solution to a second order elliptic equation with singular potentials belonging to Kato--Fefferman--Phong's class in Lipschitz domains. An elementary proof of the doubling property for $u...
On the Upper Bound of Second Eigenvalues for Uniformly Elliptic Operators of any Orders
uniformly elliptic operators of any orders
2007/12/10
r + 1. We consider the eigenvalue problems (1.1) and (1.2), and obtain Theorem 1 and Theorem 2, which generalize the results in [1,2,5].
The trace formula for transversally elliptic operators on Riemannian foliations
The trace formula transversally elliptic Riemannian foliations
2010/11/1
We prove a Duistermaat-Guillemin trace formula for transversally elliptic operators on a compact foliated manifold.