Solvability of Parabolic Regularity problem in Lebesgue spaces

勒贝格空间中抛物线正则问题的可解性

• 批准号: EP/Y033078/1
• 负责人: Martin Dindos
• 金额: $ 9.78万
• 依托单位: University of Edinburgh
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2024
• 资助国家: 英国
• 起止时间: 2024 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FY033078%2F1
• 关键词: Solvability; Parabolic; Regularity; problem; Lebesgue

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.

本文的主要目的是为解决真实的应用（如物理和工程）中经常出现的具有粗糙系数的抛物型偏微分方程问题提供新的数学思想。研究具有粗糙（或低正则性）系数的方程的动机是双重的。在许多“真实的生活”模型中，例如在材料科学中，系数可能是不连续的（例如对材料中的杂质或裂纹进行建模）。