On a new class of fractional partial differential equations II

Tien Tsan Shieh, Daniel E. Spector*


研究成果: 雜誌貢獻期刊論文同行評審

41 引文 斯高帕斯(Scopus)


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 {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.

頁(從 - 到)289-307
期刊Advances in Calculus of Variations
出版狀態已發佈 - 2018 7月 1

ASJC Scopus subject areas

  • 分析
  • 應用數學


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