標題: | On a new class of fractional partial differential equations II |
作者: | Shieh, Tien-Tsan Spector, Daniel E. 應用數學系 Department of Applied Mathematics |
關鍵字: | Fractional gradient;fractional Hardy inequality;fractional partial differential equations;interpolation;Dirichlet forms |
公開日期: | 1-七月-2018 |
摘要: | In this paper we continue to advance the theory regarding the Riesz fractional gradient in the calculus of variations and fractional partial differential equations begun in an earlier work of the same name. In particular, we here establish an L-1 Hardy inequality, obtain further regularity results for solutions of certain fractional PDE, demonstrate the existence of minimizers for integral functionals of the fractional gradient with non-linear dependence in the field, and also establish the existence of solutions to corresponding Euler-Lagrange equations obtained as conditions of minimality. In addition, we pose a number of open problems, the answers to which would fill in some gaps in the theory as well as to establish connections with more classical areas of study, including interpolation and the theory of Dirichlet forms. |
URI: | http://dx.doi.org/10.1515/acv-2016-0056 http://hdl.handle.net/11536/148069 |
ISSN: | 1864-8258 |
DOI: | 10.1515/acv-2016-0056 |
期刊: | ADVANCES IN CALCULUS OF VARIATIONS |
Volume: | 11 |
起始頁: | 289 |
結束頁: | 307 |
顯示於類別: | 期刊論文 |