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The Role of Data on the Regularity of Solutions to Some Evolution Equations

The Role of Data on the Regularity of Solutions to Some Evolution Equations

Authors :
Maria Michaela Porzio
Source :
Mathematics, Vol 12, Iss 5, p 761 (2024)
Publication Year :
2024
Publisher :
MDPI AG, 2024.

Abstract

In this paper, we study the influence of the initial data and the forcing terms on the regularity of solutions to a class of evolution equations including linear and semilinear parabolic equations as the model cases, together with the nonlinear p-Laplacian equation. We focus our study on the regularity (in terms of belonging to appropriate Lebesgue spaces) of the gradient of the solutions. We prove that there are cases where the regularity of the solutions as soon as t>0 is not influenced at all by the initial data. We also derive estimates for the gradient of these solutions that are independent of the initial data and reveal, once again, that for this class of evolution problems, the real “actors of the regularity” are the forcing terms.

Details

Language :
English
ISSN :
22277390
Volume :
12
Issue :
5
Database :
Directory of Open Access Journals
Journal :
Mathematics
Publication Type :
Academic Journal
Accession number :
edsdoj.fc43b3cc74c2405f86d03c89ab8ec1d1
Document Type :
article
Full Text :
https://doi.org/10.3390/math12050761