Academic Journal
Boundary Riesz potential estimates for parabolic equations with measurable nonlinearities
| Title: | Boundary Riesz potential estimates for parabolic equations with measurable nonlinearities |
|---|---|
| Authors: | Lee, Ho-Sik, Kim, Youchan |
| Source: | Communications in Analysis and Mechanics, Vol 17, Iss 1, Pp 61-99 (2025) |
| Publisher Information: | American Institute of Mathematical Sciences (AIMS), 2025. |
| Publication Year: | 2025 |
| Subject Terms: | riesz potentials, measurable nonlinearities, PDEs with low regular coefficients and/or low regular data, Riesz potentials, Smoothness and regularity of solutions to PDEs, Initial-boundary value problems for second-order parabolic equations, QA801-939, nonlinear parabolic equations, Analytic mechanics, Nonlinear parabolic equations, PDEs with measure, A priori estimates in context of PDEs, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) |
| Description: | We obtain a boundary pointwise gradient estimate on a parabolic half cube $ Q_{2R} \cap \{ (x^{1}, x', t) \in \mathbb{R}^{n+1} : x^{1} > 0 \} $ for nonlinear parabolic equations with measurable nonlinearities, which are only assumed to be measurable in $ x^{1} $-variable. The estimates are obtained in terms of Riesz potential of the right-hand side measure and the oscillation of the boundary data, where the boundary data is given on $ Q_{2R} \cap \{ (x^{1}, x', t) \in \mathbb{R}^{n+1} : x^{1} = 0 \} $. |
| Document Type: | Article |
| File Description: | application/xml |
| ISSN: | 2836-3310 |
| DOI: | 10.3934/cam.2025004 |
| Access URL: | https://doaj.org/article/753a5937591c43ea822c8d162ecba479 |
| Rights: | "In Copyright" Rights Statement |
| Accession Number: | edsair.doi.dedup.....978077e7fe2d7d39a3e3d615e32c7ee6 |
| Database: | OpenAIRE |
Be the first to leave a comment!