Local Gradient Estimates for Second-Order Nonlinear Elliptic and Parabolic Equations by the Weak Bernstein's Method - Institut Denis Poisson Accéder directement au contenu
Article Dans Une Revue SN Partial Differential Equations and Applications Année : 2021

Local Gradient Estimates for Second-Order Nonlinear Elliptic and Parabolic Equations by the Weak Bernstein's Method

G Barles

Résumé

In the theory of second-order, nonlinear elliptic and parabolic equations, obtaining local or global gradient bounds is often a key step for proving the existence of solutions but it may be even more useful in many applications, for example to singular perturbations problems. The classical Bernstein's method is a well-known tool to obtain these bounds but, in most cases, it has the defect of providing only a priori estimates. The ``weak Bernstein's method'', based on viscosity solutions' theory, is an alternative way to prove the global Lipschitz regularity of solutions together with some estimates but it is not so easy to perform in the case of local bounds. The aim of this paper is to provide an extension of the ``weak Bernstein's method'' which allows to prove local gradient bounds with reasonnable technicalities.
Fichier principal
Vignette du fichier
wbnl-new.pdf (164.98 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-01526740 , version 1 (23-05-2017)
hal-01526740 , version 2 (27-08-2021)

Identifiants

Citer

G Barles. Local Gradient Estimates for Second-Order Nonlinear Elliptic and Parabolic Equations by the Weak Bernstein's Method. SN Partial Differential Equations and Applications, 2021, 2 (6), ⟨10.1007/s42985-021-00130-7⟩. ⟨hal-01526740v2⟩
230 Consultations
209 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More