Let be a weak solution of a quasilinear elliptic equation of the growth with a measure right hand term . We estimate at an interior point of the domain , or an irregular boundary point , in terms of a norm of , a nonlinear potential of and the Wiener integral of . This quantifies the result on necessity of the Wiener criterion.
Starting with the computation of the appropriate Poisson kernels, we review, complement, and compare results on drifted Laplace operators in two different contexts: homogeneous trees and the hyperbolic half-plane.
In the paper the differential inequality where , , is studied. Sufficient conditions on the function are established, which guarantee nonexistence of an eventually positive solution. The generalized Riccati transformation is the main tool.
The purpose of this article is to introduce for dispersive partial differential equations with random initial data, the notion of well-posedness (in the Hadamard-probabilistic sense). We restrict the study to one of the simplest examples of such equations: the periodic cubic semi-linear wave equation. Our contributions in this work are twofold: first we break the algebraic rigidity involved in our previous works and allow much more general randomizations (general infinite product measures v.s. Gibbs...
Ce travail est consacré à l’étude du problème mixte linéaire pour un système non caractéristique, strictement hyperbolique, de degré 1, dans le cas où la condition aux limites présente un saut sur une hypersurface non caractéristique du bord. Sous la condition de Lopatinski uniforme hors de cette hypersurface et sous une hypothèse supplémentaire le long de celle-ci, on prouve un résultat d’existence et d’unicité dans l’espace de Sobolev . On étudie ensuite la propagation de la régularité conormale...