Browsing by Author "Ponce, Augusto C."

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A Decomposition by Non-Negative Functions in the Sobolev Space W-k,W-1
(2020-01-01)
Ponce, Augusto C.
;
Spector, Daniel
;
應用數學系
;
Department of Applied Mathematics
We show how a strong capacitary inequality can be used to give a decomposition of any function in the Sobolev space W-k,W-1 (R-d) as the difference of two non-negative functions in the same space with control of their norms.
A note on the fractional perimeter and interpolation
(2017-09-01)
Ponce, Augusto C.
;
Spector, Daniel
;
應用數學系
;
Department of Applied Mathematics
We present the fractional perimeter as a set-function interpolation between the Lebesgue measure and the perimeter in the sense of De Giorgi. Our motivation comes from a new fractional Boxing inequality that relates the fractional perimeter and the Hausdorff content and implies several known inequalities involving the Gagliardo seminorm of the Sobolev spaces W-alpha,W-1 of order 0 < alpha < 1. (C) 2017 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.
L On formulae decoupling the total variation of BV functions
(2017-05-01)
Ponce, Augusto C.
;
Spector, Daniel
;
應用數學系
;
Department of Applied Mathematics
In this paper we prove several formulae that enable one to capture the singular portion of the measure derivative of a function of bounded variation as a limit of non-local functionals. One special case shows that rescalings of the fractional Laplacian of a function u is an element of SBV converge strictly to the singular portion of D-u. (C) 2016 Elsevier Ltd. All rights reserved.