Stochastic calculus and degenerate boundary value problems

Patrick Cattiaux

Displaying similar documents to “Stochastic calculus and degenerate boundary value problems”

Oblique derivative problems and invariant measures

I. Capuzzo Dolcetta, M. G. Garroni (1986)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Similarity:

Capacitary strong type estimates in semilinear problems

D. Adams, Michel Pierre (1991)

Annales de l'institut Fourier

Similarity:

We prove the equivalence of various capacitary strong type estimates. Some of them appear in the characterization of the measures $μ$ that are admissible data for the existence of solutions to semilinear elliptic problems with power growth. Other estimates are known to characterize the measures $μ$ for which the Sobolev space $W^{2, p}$ can be imbedded into $L^{p} (μ)$ . The motivation comes from the semilinear problems: simpler descriptions of admissible data are given. The proof surprisingly involves the...

On boundary integral equations of the first kind for the bi-laplacian in a polygonal plane domain

Martin Costabel, Ernst Stephan, Wolfgang L. Wendland (1983)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Similarity:

Ergodicity for the stochastic complex Ginzburg–Landau equations

Cyril Odasso (2006)

Annales de l'I.H.P. Probabilités et statistiques

Similarity:

On singular perturbation problems with Robin boundary condition

Henri Berestycki, Juncheng Wei (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Similarity:

We consider the following singularly perturbed elliptic problem $\begin{matrix} ϵ^{2} Δ u - u + f (u) & = 0, u > 0 in Ω, \\ ϵ \frac{\partial u}{\partial ν} + λ u & = 0 on \partial Ω, \end{matrix}$ where $f$ satisfies some growth conditions, $0 \leq λ \leq + \infty$ , and $Ω \subset ℝ^{N}$ ( $N > 1$ ) is a smooth and bounded domain. The cases $λ = 0$ (Neumann problem) and $λ = + \infty$ (Dirichlet problem) have been studied by many authors in recent years. We show that, there exists a generic constant $λ_{*} > 1$ such that, as $ϵ \to 0$ , the least energy solution has a spike near the boundary if $λ \leq λ_{*}$ , and has an interior spike near the innermost part of the domain if $λ > λ_{*}$ . Central...

On iterations of Green type integrals for matrix factorizations of the Laplace operator

Alexandre A. Shlapunov (1994)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Similarity:

Convergence of special Green integrals for matrix factorization of the Laplace operator in $R^{n}$ is proved. Explicit formulae for solutions of $\bar{\partial}$ -equation in strictly pseudo-convex domains in $C^{n}$ are obtained.