Many authors have considered this problem, specially in the case p= 2, in the form cf. eg
[BBC],[BS],[BG1]. We are interested here in the case 1 p N. The case p &# x3E; N offers less …

An interesting phenomenon in water channels is the appearance of waves with length much
greater than the depth of the water. In 1895 DJ Korteweg and G. de Vries started the …

Traditional deep learning-based image dehazing methods usually use the high-level
features (which contain more semantic information) to remove haze in the input image, while …

The past twenty years have witnessed a tremendous development of the theory of boundary
value problems for semilinear elliptic equations-positive solutions. We do not intend to …

This article is one in a series by the authors to study some qualitative properties of positive
solutions of elliptic second order boundary value problems of the type in various kinds of …

Here we study, on a connected domain ΩcR", the zero set u~ ι {0} of a solution u of an elliptic
equation aijDjDjU+ bjDjU+ cu= 0, where aij, bj, c are bounded and#/7 is continuous. Our …

The Minkowski Problem concerns the existence, uniqueness, and regularity of closed
convex hypersurfaces whose Gauss curvature (as a function of the outer normals) is …

Christodoulou, D.; Klainerman, S. The global nonlinear stability of the Minkowski space.
Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi" Séminaire Goulaouic …

We establish interior Schauder estimates for kinetic equations with integrodifferential
diffusion. We study equations of the form f t+ v⋅∇ xf= ℒ v f+ c, where ℒ v is an …

We consider certain families of Dirichlet forms of diffusion type that describe the variational
behaviour of possibly highly nonhomogeneous and nonisotropic bodies and we prove a …