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

Maria Michaela Porzio ()
Additional contact information
Maria Michaela Porzio: Dipartimento di Pianificazione, Design, Tecnologia dell’Architettura, Sapienza Universitá di Roma, via Flaminia 72, 00196 Roma, Italy

Mathematics, 2024, vol. 12, issue 5, 1-12

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.

Keywords: regularity of solutions; p-Laplacian equation; nonlinear degenerate parabolic equations; smoothing effect; heat equation; gradient estimates (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/5/761/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/5/761/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:5:p:761-:d:1350775

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().