Academic Journal

Boundary Riesz potential estimates for parabolic equations with measurable nonlinearities

Bibliographic Details
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
Description
ISSN:28363310
DOI:10.3934/cam.2025004