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Advanced Nonlinear Studies

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Volume 18, Issue 2


On a Class of Quasilinear Elliptic Equations with Degenerate Coerciveness and Measure Data

Flavia Smarrazzo
Published Online: 2017-09-27 | DOI: https://doi.org/10.1515/ans-2017-6032


We study the existence of measure-valued solutions for a class of degenerate elliptic equations with measure data. The notion of solution is natural, since it is obtained by a regularization procedure which also relies on a standard approximation of the datum μ. We provide partial uniqueness results and qualitative properties of the constructed solutions concerning, in particular, the structure of their diffuse part with respect to the harmonic-capacity.

Keywords: Measure-Valued Solutions; Degenerate Elliptic Equations; Radon Measures

MSC 2010: 35J15; 35D30; 28A33


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About the article

Received: 2017-06-02

Revised: 2017-08-27

Accepted: 2017-08-29

Published Online: 2017-09-27

Published in Print: 2018-04-01

Citation Information: Advanced Nonlinear Studies, Volume 18, Issue 2, Pages 361–392, ISSN (Online) 2169-0375, ISSN (Print) 1536-1365, DOI: https://doi.org/10.1515/ans-2017-6032.

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