Browsing by Author "Schikorra, Armin"

Now showing 1 - 3 of 3

An L-1-type estimate for Riesz potentials
(2017-01-01)
Schikorra, Armin
;
Spector, Daniel
;
Van Schaftingen, Jean
;
應用數學系
;
Department of Applied Mathematics
In this paper we establish new L-1-type estimates for the classical Riesz potentials of order alpha is an element of (0, N): parallel to I alpha u parallel to N-L/(N-alpha)(R-N) <= C parallel to Ru parallel to (L1(RN; RN)). This sharpens the result of Stein and Weiss on the mapping properties of Riesz potentials on the real Hardy space H-1 (R-N) and provides a new family of L-1-Sobolev inequalities for the Riesz fractional gradient.
L-p theory for fractional gradient PDE with VMO coefficients
(2015-01-01)
Schikorra, Armin
;
Shieh, Tien-Tsan
;
Spector, Daniel
;
交大名義發表
;
National Chiao Tung University
In this paper, we prove L-p estimates for the fractional derivatives of solutions to elliptic fractional partial differential equations whose coefficients are VMO. In particular, our work extends the optimal regularity known in the second order elliptic setting to a spectrum of fractional order elliptic equations.
Regularity for a fractional p-Laplace equation
(2018-02-01)
Schikorra, Armin
;
Shieh, Tien-Tsan
;
Spector, Daniel E.
;
應用數學系
;
Department of Applied Mathematics
In this note, we consider regularity theory for a fractional p-Laplace operator which arises in the complex interpolation of the Sobolev spaces, the H-s,H-p-Laplacian. We obtain the natural analogue to the classical p-Laplacian situation, namely C-loc(s+alpha)-regularity for the homogeneous equation.