The first two chapters contain introductory courses. Chapter 1 presents the theory of Sobolev-
type spaces Hs (s∈ R) on Rn, on a smooth closed manifold, and on a smooth bounded …

Эта книга адресуется математикам, которые занимаются уравнениями в частных
производных и функциональным анализом. Первые две главы содержат вводные …

We consider the exit event from a metastable state for the overdamped Langevin dynamics
dX_t=-∇ f (X_t) dt+ h dB_t d X t=-∇ f (X t) dt+ hd B t. Using tools from semiclassical analysis …

We introduce certain Sobolev-Besov spaces which are particularly well adapted for
measuring the smoothness of data and solutions of mixed boundary value problems in …

We prove that given any k∈ N, for each open set Ω⊆ R n and any closed subset D of Ω¯
such that Ω is locally an (ε, δ)-domain near∂ Ω∖ D, there exists a linear and bounded …

We study boundary-value problems with mixed boundary conditions in weakly Lipschitz
domains of compact boundaryless Riemannian Lipschitz manifolds. These include the case …

This paper is devoted to some transmission problems for the Laplace and linear elasticity
operators in two-and three-dimensional nonsmooth domains. We investigate the behaviour …

Inequalities for the eigenvalues of the (negative) Laplacian subject to mixed boundary
conditions on polyhedral and more general bounded domains are established. The …

We study several different aspects of the energy equipartition principle for water waves. We
prove a virial identity that implies that the potential energy is equal, on average, to a …

Some recent methods for lossy signal and image compression store only a few selected
pixels and fill in the missing structures by inpainting with a partial differential equation (PDE) …