1,720,984 research outputs found
On some partial differential equation for non coercive functional and critical Sobolev exponent
No full textInternational audienceWe consider the Dirichlet Problem for equations involving the Laplacian in the case "beyond the first eigenvalue" and with right hand side with critical growth
Existence et régularité pour les solutions d'une équation Complètement non linéaire sur le modèle du pseudo Laplacien.
No full textInternational audienceThis paper is devoted to the existence and Lipschitz regularity of viscosity solutions for a class of very degenerate fully nonlinear operators, on the model of the pseudo p-Laplacian. We also prove a strong maximum principle.Dans cet artcile on montre des résultats d'existence et de régularité pour les solutions d'une classe d'équations complètement non linéaires très dégénérées, sur le modèle de l'équation du pseudo Laplacien
Regularity and uniqueness of the first eigenfunction for singular fully noninear equations
No full text22 pages, no pictureInternational audienceFor singular fully nonlinear operators we prove that the eigenfunctions corresponding to the principal eigenvalues in bounded domains are simple
Eigenvalue and Dirichlet problem for fully-nonlinear operators in non smooth domains
No full text20 pages no pictureInternational audienceWe study the maximum principle, the existence of eigenvalue and the existence of solution for the Dirichlet problem relative to operators which are fully-nonlinear, elliptic but presenting some singularity or degeneracy which are similar to those of the p-Laplacian, we consider the equations in bounded domains which only satisfy the exterior cone condition
One-dimensional symmetry for solutions of Allen Cahn fully nonlinear equations.
No full text16 pages, no pictureInternational audienceThis article presents some qualitative results for solutions of the fully nonlinear elliptic equation F(∇u,D2u) + f(u) = 0 in IRN. Precisely under some additional assumptions on f, if −1 ≤ u ≤ 1 and limx1→±∞ u(x1,x′) = ±1 uniformly with respect to x′, then the solution depends only on x1
Regularity and uniqueness of the first eigenfunction for singular fully noninear equations
No full text22 pages, no pictureInternational audienceFor singular fully nonlinear operators we prove that the eigenfunctions corresponding to the principal eigenvalues in bounded domains are simple
Regularity for radial solutions of degenerate fully nonlinear equations}
No full text13 pages, no pictureInternational audienceIn this paper we prove the C1,β regularity of radial solutions for fully nonlinear degenerate elliptic equations
EIGENVALUE, MAXIMUM PRINCIPLE AND REGULARITY FOR FULLY NON LINEAR HOMOGENEOUS OPERATORS
No full text32pages no pictureInternational audienceThe main scope of this article is to define the concept of principal eigenvalue for fully non linear second order operators in bounded domains that are elliptic, homogenous with lower order terms. In particular we prove maximum and comparison principle, H ̈older and Lipschitz regularity. This leads to the existence of a first eigenvalue and eigenfunction and to the existence of solutions of Dirichlet problems within this class of operators
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