arXiv subjects

Francoise Demengel

Publications and source records attributed to Francoise Demengel.

11 recordsLinked to original sources

arXiv2021

Mixed boundary value problems for fully nonlinear degenerate or singular equations

We prove existence, uniqueness and regularity results for mixed boundary value problems associated with fully nonlinear, possibly singular or degenerate elliptic equations. Our main result is a global Hölder estimate for solutions, obtained by means of the comparison principle and the construction of ad hoc barriers. The global Hölder estimate immediately yields a compactness result in the space of solutions, which could be applied in the study of principal eigenvalues and principal eigenfunctions of mixed boundary value problems.

math.AP↗

arXiv2019

A Liouville theorem for fully nonlinear problems with infinite boundary conditions and applications

We prove a Liouville type classification theorem in half-spaces for infinite boundary value problems related to fully nonlinear, uniformly elliptic operators. We then apply the result in order to obtain gradient boundary blow up rates for ergodic functions in bounded domains related to degenerate/singular operators, and, as a further consequence, we deduce the uniqueness of the ergodic functions.

math.AP↗

arXiv2019

${\cal C}^{1, γ} $ regularity for singular or degenerate fully nonlinear operators and applications

In this note, we prove $\mathcal{C}^{1,γ}$ regularity for solutions of some fully nonlinear degenerate elliptic equations with "superlinear" and "subquadratic " Hamiltonian terms. As an application, we complete the results of \cite{BDL1} concerning the associated ergodic problem, proving, among other facts, the uniqueness, up to constants, of the ergodic function.

math.AP↗

arXiv2018

Dirichlet problems for fully nonlinear equations with \lq subquadratic \lq Hamiltonians

For a class of fully nonlinear equations having second order operators which may be singular or degenerate when the gradient of the solutions vanishes, and having first order terms with power growth, we prove the existence and uniqueness of suitably defined viscosity solution of Dirichlet problem and we further show that it is a Lipschitz continuous function.

math.AP↗

arXiv2017

Ergodic pairs for singular or degenerate fully nonlinear operators

We study the ergodic problem for fully nonlinear operators which may be singular or degenerate when the gradient of solutions vanishes. We prove the convergence of both explosive solutions and solutions of Dirichlet problems for approximating equations. We further characterize the ergodic constant as the infimum of constants for which there exist bounded sub solutions. As intermediate results of independent interest, we prove a priori Lipschitz estimates depending only on the norm of the zeroth order term, and a comparison principle for equations having no zero order terms.

math.AP↗

arXiv2016

Lipschitz Interior regularity for the viscosity and weak solutions of the pseudo-$p$Laplacian

We prove interior Lipschitz regularity result for weak and viscosity solutions of the pseudo $p$Laplacien $(p-1)\sum_i |\partial_i u|^{p-2} \partial_{ii} u = f$ for $p>2$ and $f$ bounded.

math.AP↗

arXiv2015

Existence and regularity results for Fully Non Linear Operators on the model of the pseudo Pucci's operators

In this article we prove some Lipschitz estimates and existence result for a class of degenerate fully nonlinear elliptic equations which are a generalization of the pseudo p-Laplacian. The operators are degenerate elliptic at any point where even only one partial derivative of the solution is zero.

math.AP↗

arXiv2009

Regularity and uniqueness of the first eigenfunction for singular fully non linear operators

In this article we prove that solutions of singular fully nonlinear partial differential equations are $C^{1,β}$. We also prove the simplicity of the principal eigenvalues for the Dirichlet Problem associated to these operators using that regularity, a strict comparison principle and Sard's theorem.

math.AP↗

arXiv2009

Eigenfunctions for singular fully non linear equations in unbounded domains

In this paper we prove some Harnack inequality for fully non linear degenerate elliptic equations, in the two dimensional case, extending the results of Davila Felmer and Quaas in the singular case but in all dimensions. We then apply this result for the existence of an eigenfunction in smooth bounded domain.

math.AP↗

arXiv2009

Generalized eigenvalues for fully tnonlinear singular or degenerate operators in the radial case

In this paper we extend some existence's results concerning the generalized eigenvalues for fully nonlinear operators singular or degenerate. We consider the radial case and we prove the existence of an infinite number of eigenvalues, simple and isolated. This completes the results obtained by the author with Isabeau Birindelli for the first eigenvalues in the radial case, and the results obtained for the Pucci's operator by Busca Esteban and Quaas and for the $p$-Laplace operator by Del Pino and Manasevich.

math.AP↗

arXiv2009

Existence results for parabolic problems related to fully non linear operators degenerate or singular

In this paper we prove some existence and regularity results concerning parabolic equations dtu = F(D u, D2 u) + f(x,u) with some boundary conditions, on Omega times ]0,T[, where Omega is some bounded domain which possesses the cone property and $F$ is singular or degenerate, with some uniform ellipticity conditions.

math.AP↗