Research
Title : | Regularity estimates for elliptic systems of differential forms |
Area of research : | Mathematical Sciences |
Focus area : | Nonlinear Potential Theory, Elliptic Partial Differential Equations |
Principal Investigator : | Dr. Swarnendu Sil, Indian Institute Of Science, Bangalore, Karnataka |
Timeline Start Year : | 2024 |
Timeline End Year : | 2027 |
Contact info : | swarnendusil@iisc.ac.in |
Details
Executive Summary : | The basic goal of the project is to develop a nonlinear potential theory for quasilinear systems of vector-valued differential forms, which generalises both the p-Laplace equation, p-Laplacian system and the p-curl curl operator that appears in the context of electromagnetism and fluid mechanics. Such theory for p-Laplace equation is well-developed and is being actively developed for the p-Laplacian systems. But these methods can not be applied either to the p-curl curl operator or the general case of vector-valued forms. The plan is to develop methods that is adapted to the exterior algebra structure and can handle the additional difficulties created by the non-ellipticity of the operators. |
Total Budget (INR): | 6,60,000 |
Organizations involved
Implementing Agency : | Indian Institute Of Science, Bangalore, Karnataka Funding Agency :Anusandhan National Research Foundation/ Science and Engineering Research Board | Source :Anusandhan National Research Foundation/Science and Engineering Research Board (SERB), DST 2023-24 | |