Solvability of Parabolic Regularity problem in Lebesgue spaces
Lead Research Organisation:
University of Edinburgh
Department Name: Sch of Mathematics
Abstract
The main objective of this proposal is to meet this need and develop novel mathematical ideas for parabolic partial differential equations with rough coefficients which occur frequently in real applications (such as physics and engineering).
In recent years substantial progress has been achieved in our understanding of partial differential equations with rough coefficients and associated boundary value problems. The motivation to study equations with rough (or low regularity) coefficients is twofold. In many "real life" models, such as in materials science, the coefficients can be discontinuous (for example modelling impurities in the materials or cracks).
The proposal addresses one aspect from wide field of open problems that concerns the Regularity problem for these equations.
In recent years substantial progress has been achieved in our understanding of partial differential equations with rough coefficients and associated boundary value problems. The motivation to study equations with rough (or low regularity) coefficients is twofold. In many "real life" models, such as in materials science, the coefficients can be discontinuous (for example modelling impurities in the materials or cracks).
The proposal addresses one aspect from wide field of open problems that concerns the Regularity problem for these equations.
Organisations
Publications
Dindoš M
(2025)
On the Regularity Problem for Parabolic Operators and the Role of Half-Time Derivative
in The Journal of Geometric Analysis
| Description | Parabolic partial differential equations appear in many areas of interests to modern life such as physics, mechanics, applied mathematics and science as a whole. Hence understanding of their solutions and behaviour is the key to further development of these disciplines. This project has achieved such progress and has unlocked a better our understanding of a parabolic boundary value problem for operators with rough coefficients (these are important to model for example materials with inhomogeneities or modelling transitions between two different materials). |
| Exploitation Route | The research output is currently in a review process, but is already disseminated at research talks and conferences. |
| Sectors | Other |
| URL | https://arxiv.org/abs/2410.23801 |