Intrinsic geometry and De Giorgi classes for certain anisotropic problems

Paolo Baroni; Agnese Di Castro; Giampiero Palatucci

doi:10.3934/dcdss.2017032

Article Contents

2017, Volume 10, Issue 4: 647-659. Doi: 10.3934/dcdss.2017032

This issue Previous Article Preface Next Article The Dirichlet-to-Neumann map for Schrödinger operators with complex potentials

Intrinsic geometry and De Giorgi classes for certain anisotropic problems

1.
Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Università di Parma, Campus -Parco Area delle Scienze 53/A, 43124 Parma, Italy
2.
Dipartimento di Scienze di Base e Applicate per l'Ingegneria, Sapienza Università di Roma, Via A. Scarpa 14, 00162 Roma, Italy

^* Corresponding author: Giampiero Palatucci
^* Corresponding author: Giampiero Palatucci

Received: December 31, 2015

Revised: June 30, 2016

Published: July 2017

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Abstract

We analyze a natural approach to the regularity of solutions of problems related to some anisotropic Laplacian operators, and a subsequent extension of the usual De Giorgi classes, by investigating the relation of the functions in such classes with the weak solutions to some anisotropic elliptic equations as well as with the quasi-minima of the corresponding functionals with anisotropic polynomial growth.

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Mathematics Subject Classification: Primary: 35J70; Secondary: 35B50, 35B65, 49N60.

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