35 citations · 165 across the 26 of their papers we have counts for
6 papers · 1 filter
An -type estimate for Riesz potentials
Armin Schikorra, Daniel Spector, Jean Van Schaftingen
In this paper we establish new -type estimates for the classical Riesz potentials of order : \[ \|I_αu\|_{L^{N/(N-α)}(\mathbb{R}^N)} \leq C \|Ru\|_{L^1(\mathbb{R}…
Analysis and Application of a non-local Hessian
Jan Lellmann, Konstantinos Papafitsoros, Carola Schoenlieb +1
In this work we introduce a formulation for a non-local Hessian that combines the ideas of higher-order and non-local regularization for image restoration, extending the idea of no…
A Leray-Trudinger Inequality
Georgios Psaradakis, Daniel Spector
We consider a multidimensional version of an inequality due to Leray as a substitute for Hardy's inequality in the case In this paper we provide an optimal Sobolev-type…
On the role of Riesz potentials in Poisson's equation and Sobolev embeddings
Rahul Garg, Daniel Spector
In this paper, we study the mapping properties of the classical Riesz potentials acting on -spaces. In the supercritical exponent, we obtain new "almost" Lipschitz continuity…
On regularity of solutions to Poisson's equation
Rahul Garg, Daniel Spector
In this note, we announce new regularity results for some locally integrable distributional solutions to Poisson's equation. This includes, for example, the standard solutions obta…
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…