14 citations · 14 across the 3 of their papers we have counts for
5 papers
On a new class of fractional partial differential equations II
Daniel Spector, Tien-Tsan Shieh
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 earl…
Regularity for a fractional p-Laplace equation
Armin Schikorra, Tien-Tsan Shieh, Daniel Spector
In this note we consider regularity theory for a fractional -Laplace operator which arises in the complex interpolation of the Sobolev spaces, the -Laplacian. We obtain…
Ground state patterns and phase transition of spin-1 Bose-Einstein condensates via Γ-convergence theory
I-Liang Chern, Chiu-Fen Chou, Tien-Tsan Shieh
We develop an analytic theory for the ground state patterns and their phase transitions for spin-1 Bose-Einstein condensates on a bounded domain in the presence of a uniform magnet…
-theory for fractional gradient PDE with VMO coefficients
Armin Schikorra, Tien-Tsan Shieh, Daniel Spector
In this paper, we prove estimates for the fractional derivatives of solutions to elliptic fractional partial differential equations whose coefficients are . In particula…
On a new class of fractional partial differential equations
Tien-Tsan Shieh, Daniel Spector
In this paper, we study a new class of fractional partial differential equations which are obtained by minimizing variational problems in fractional Sobolev spaces. We introduce a…