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Limit of 𝑝-Laplacian obstacle problems

  • Raffaela Capitanelli ORCID logo EMAIL logo and Maria Agostina Vivaldi ORCID logo
Published/Copyright: April 15, 2020

Abstract

In this paper, we study asymptotic behavior of solutions to obstacle problems for p-Laplacians as p . For the one-dimensional case and for the radial case, we give an explicit expression of the limit. In the n-dimensional case, we provide sufficient conditions to assure the uniform convergence of the whole family of the solutions of obstacle problems either for data f that change sign in Ω or for data f (that do not change sign in Ω) possibly vanishing in a set of positive measure.


Communicated by Hitoshi Ishii


Award Identifier / Grant number: RM11715C7D9096AD

Funding statement: The authors are members of GNAMPA (INdAM) and are partially supported by Grant Ateneo “Sapienza” 2017.

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Received: 2019-07-15
Revised: 2020-01-07
Accepted: 2020-03-24
Published Online: 2020-04-15
Published in Print: 2022-04-01

© 2020 Walter de Gruyter GmbH, Berlin/Boston

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