4 papers
Weighted Perimeters and pth Moments of Inertia of Convex Curves and Surfaces
Gyula Csató, Davide Giovagnoli, Prosenjit Roy
We study a shape optimization problem among convex bodies in that minimize or maximize weighted perimeters of the form $\int_{\partialΩ} ϕ(|x|) \, \mathrm{d} H^{n-1}…
Examples of optimal Hölder regularity in semilinear equations involving the fractional Laplacian
Gyula Csató, Albert Mas
We discuss the Hölder regularity of solutions to the semilinear equation involving the fractional Laplacian in one dimension. We put in evidence a new regularity ph…
Strict rearrangement inequalities: nonexpansivity and periodic Gagliardo seminorms
Gyula Csató, Albert Mas
This paper deals with the behavior of the periodic Gagliardo seminorm under two types of rearrangements, namely under a periodic, and respectively a cylindrical, symmetric decreasi…
A fractional Hardy-Sobolev inequality of Michael-Simon type on convex hypersurfaces
Gyula Csató, Prosenjit Roy
In this paper we prove a fractional version of a Caffarelli-Kohn-Nirenberg type interpolation inequality on hypersurfaces which are boundaries of convex sets. Th…