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Advances in Calculus of Variations

Managing Editor: Duzaar, Frank / Kinnunen, Juha

Editorial Board Member: Armstrong, Scott N. / Astala, Kari / Colding, Tobias / Dacorogna, Bernard / Dal Maso, Gianni / DiBenedetto, Emmanuele / Fonseca, Irene / Finster, Felix / Gianazza, Ugo / Gursky, Matthew / Hardt, Robert / Ishii, Hitoshi / Kristensen, Jan / Manfredi, Juan / Martell, Jose Maria / McCann, Robert / Mingione, Giuseppe / Nystrom, Kaj / Pacard, Frank / Preiss, David / Riviére, Tristan / Schaetzle, Reiner / Silvestre, Luis

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IMPACT FACTOR 2016: 1.182

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1864-8266
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On certain anisotropic elliptic equations arising in congested optimal transport: Local gradient bounds

Lorenzo Brasco / Guillaume Carlier
Published Online: 2013-06-28 | DOI: https://doi.org/10.1515/acv-2013-0007

Abstract.

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: x(|ux|-δ1)+q-1ux|ux|+y(|uy|-δ2)+q-1uy|uy|=f, for 2q< and some non-negative parameters δ1,δ2. Here (·)+ stands for the positive part. We prove that if fL loc , then uL loc r for every r ≥ 1.

Keywords: Degenerate elliptic equations; anisotropic problems; traffic congestion

MSC: 35J70; 35B65; 49K20

About the article

Received: 2013-02-28

Revised: 2013-06-14

Accepted: 2013-06-20

Published Online: 2013-06-28

Published in Print: 2014-07-01


Funding Source: ANR

Award identifier / Grant number: ANR-09-JCJC-0096-01 EVAMEF

Funding Source: ANR

Award identifier / Grant number: ANR-07-BLAN-0235 OTARIE

Funding Source: ERC

Award identifier / Grant number: Advanced Grant No. 226234


Citation Information: Advances in Calculus of Variations, ISSN (Online) 1864-8266, ISSN (Print) 1864-8258, DOI: https://doi.org/10.1515/acv-2013-0007.

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