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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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1864-8266
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The Dirichlet problem for a singular elliptic equation arising in the level set formulation of the inverse mean curvature flow

José M. Mazón / Sergio Segura de León
Published Online: 2013-04-01 | DOI: https://doi.org/10.1515/acv-2011-0001

Abstract.

In the present paper we consider the Dirichlet problem associated with a nonlinear singular elliptic equation whose differential operator arises in the level set formulation of the inverse mean curvature flow; namely, we study

We introduce a suitable concept of weak solution, for which we prove existence and uniqueness of the homogeneous Dirichlet problem in a bounded open set of ℝN for data f belonging to suitable Lebesgue spaces. Moreover, examples of explicit solutions are shown.

Keywords: p-Laplacian; total variation; inverse mean curvature flow

About the article

Received: 2011-06-20

Revised: 2012-03-12

Accepted: 2012-04-04

Published Online: 2013-04-01

Published in Print: 2013-04-01


Citation Information: Advances in Calculus of Variations, ISSN (Online) 1864-8266, ISSN (Print) 1864-8258, DOI: https://doi.org/10.1515/acv-2011-0001.

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© 2013 by Walter de Gruyter Berlin Boston. Copyright Clearance Center

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[3]
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