On a new class of fractional partial differential equations II

By Tien-Tsan Shieh, Daniel Spector. Advances in Calculus of Variations, 2016

96 citations recorded by the source corpus.

Abstract 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.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4013f63b2a5c97ff710fc7f49d3509a18fb9c988

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In Applied Mathematics

1. Javier Cueto
2. C. Mora‐Corral
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In Mathematical Physics

1. Javier Cueto
2. C. Mora‐Corral
3. José Carlos Bellido

Citations in the corpus

• Fractional Piola identity and polyconvexity in fractional spaces (2018, methodology): “References [32, 33] deal with integral functionals of the form”