• français
    • English
  • English 
    • français
    • English
  • Login
JavaScript is disabled for your browser. Some features of this site may not work without it.
BIRD Home

Browse

This CollectionBy Issue DateAuthorsTitlesSubjectsJournals BIRDResearch centres & CollectionsBy Issue DateAuthorsTitlesSubjectsJournals

My Account

Login

Statistics

View Usage Statistics

On certain anisotropic elliptic equations arising in congested optimal transport: local gradient bounds

Thumbnail
Date
2013
Link to item file
http://hal.archives-ouvertes.fr/hal-00722615
Dewey
Analyse
Sujet
Traffic congestion; Anisotropic problems; Degenerate elliptic equations
Journal issue
Advances in Calculus of Variations
Volume
7
Number
3
Publication date
2013
Article pages
379–407
Publisher
De Gruyter
DOI
http://dx.doi.org/10.1515/acv-2013-0007
URI
https://basepub.dauphine.fr/handle/123456789/9874
Collections
  • CEREMADE : Publications
Metadata
Show full item record
Author
Carlier, Guillaume
Brasco, Lorenzo
Type
Article accepté pour publication ou publié
Abstract (EN)
Motivated by applications to congested optimal transport problems, we prove higher integrability results for the gradient of solutions to some anisotropic elliptic equations, exhibiting a wide range of degeneracy. The model case we have in mind is the following: \[ \partial_x \left[(|u_{x}|-\delta_1)_+^{q-1}\, \frac{u_{x}}{|u_{x}|}\right]+\partial_y \left[(|u_{y}|-\delta_2)_+^{q-1}\, \frac{u_{y}}{|u_{y}|}\right]=f, \] for $2\le q<\infty$ and some non negative parameters $\delta_1,\delta_2$. Here $(\,\cdot\,)_+$ stands for the positive part. We prove that if $f\in L^\infty_{loc}$, then $\nabla u\in L^r_{loc}$ for every $r\ge 1$.

  • Accueil Bibliothèque
  • Site de l'Université Paris-Dauphine
  • Contact
SCD Paris Dauphine - Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16

 Content on this site is licensed under a Creative Commons 2.0 France (CC BY-NC-ND 2.0) license.