-boundedness of oscillating spectral multipliers on Riemannian manifolds
We prove endpoint estimates for operators given by oscillating spectral multipliers on Riemannian manifolds with -bounded geometry and nonnegative Ricci curvature.
-inequalities for the laplacian and unique continuation
We prove an inequality of the typeThis is then used to derive the unique continuation property for the differential inequality under suitable local integrability assumptions on the function .
L2-Integrability of Second Order Derivatives for Poisson's Equation in Nonsmooth Domains.
La première valeur propre du laplacien pour le problème de Dirichlet
Laplace equation in the half-space with a nonhomogeneous Dirichlet boundary condition
We deal with the Laplace equation in the half space. The use of a special family of weigted Sobolev spaces as a framework is at the heart of our approach. A complete class of existence, uniqueness and regularity results is obtained for inhomogeneous Dirichlet problem.
Laplace type operators: Dirichlet problem
We investigate Laplace type operators in the Euclidean space. We give a purely algebraic proof of the theorem on existence and uniqueness (in the space of polynomial forms) of the Dirichlet boundary problem for a Laplace type operator and give a method of determining the exact solution to that problem. Moreover, we give a decomposition of the kernel of a Laplace type operator into -irreducible subspaces.
Le comportement de la résolvante modifiée du laplacien pour des obstacles captifs
Le problème de Dirichlet dans l’espace
Le problème de Pompeiu
Linearization and explicit solutions of the minimal surface equations.
We show that the apparatus of support functions, usually used in convex surfaces theory, leads to the linear equation Δh + 2h = 0 describing locally germs of minimal surfaces. Here Δ is the Laplace-Beltrami operator on the standard two-dimensional sphere. It explains the existence of the sum operator of minimal surfaces, introduced recently. In 4-dimensional space the equation Δ h + 2h = 0 becomes inequality wherever the Gauss curvature of a minimal hypersurface is nonzero.
Local uniform convergence of the Riesz means of Laplace and Dirac expansions
Locking effects in the finite element approximation of elasticity problems.
Lösung des Dirichlet Problems bei Jordangebieten mit analytischem Rand durch Interpolation.
Lower and upper bounds for the Rayleigh conductivity of a perforated plate
Lower and upper bounds for the Rayleigh conductivity of a perforation in a thick plate are usually derived from intuitive approximations and by physical reasoning. This paper addresses a mathematical justification of these approaches. As a byproduct of the rigorous handling of these issues, some improvements to previous bounds for axisymmetric holes are given as well as new estimates for tilted perforations. The main techniques are a proper use of the Dirichlet and Kelvin variational principlesin...