scholarly journals A quantitative version of the isoperimetric inequality: the anisotropic case

2009 ◽  
pp. 619-651
Author(s):  
Luca Esposito ◽  
Nicola Fusco ◽  
Cristina Trombetti
Keyword(s):  
Isoperimetric Inequality ◽  
Quantitative Version ◽  
Anisotropic Case

scholarly journals Isoperimetric problems for a nonlocal perimeter of Minkowski type

2017 ◽  
Vol 2 (1) ◽  
Author(s):  
Annalisa Cesaroni ◽  
Matteo Novaga
Keyword(s):  
Isoperimetric Inequality ◽  
Repulsive Interaction ◽  
Isoperimetric Problems ◽  
Quantitative Version ◽  
Interaction Terms ◽  
Existence Of Minimizers ◽  
Non Local

AbstractWe show a quantitative version of the isoperimetric inequality for a non local perimeter of Minkowski type. We also apply this result to study isoperimetric problems with repulsive interaction terms, under volume and convexity constraints.We prove existence of minimizers, and we describe their shape as the volume tends to zero or to infinity.

A quantitative isoperimetric inequality on the sphere

2017 ◽  
Vol 10 (3) ◽  
pp. 223-265 ◽  
Author(s):  
Verena Bögelein ◽  
Frank Duzaar ◽  
Nicola Fusco
Keyword(s):  
Isoperimetric Inequality ◽  
Constant Independent ◽  
Quantitative Version

AbstractIn this paper we prove a quantitative version of the isoperimetric inequality on the sphere with a constant independent of the volume of the set E.

Multi-parameter Singular Integrals. (AM-189)

2017 ◽  
Author(s):  
Brian Street
Keyword(s):  
Partial Differential Equations ◽  
Graduate Students ◽  
General Theory ◽  
Differential Equations ◽  
Singular Integrals ◽  
Main Tool ◽  
Classical Theorem ◽  
Quantitative Version ◽  
Linear Partial Differential Equations

This book develops a new theory of multi-parameter singular integrals associated with Carnot–Carathéodory balls. The book first details the classical theory of Calderón–Zygmund singular integrals and applications to linear partial differential equations. It then outlines the theory of multi-parameter Carnot–Carathéodory geometry, where the main tool is a quantitative version of the classical theorem of Frobenius. The book then gives several examples of multi-parameter singular integrals arising naturally in various problems. The final chapter of the book develops a general theory of singular integrals that generalizes and unifies these examples. This is one of the first general theories of multi-parameter singular integrals that goes beyond the product theory of singular integrals and their analogs. This book will interest graduate students and researchers working in singular integrals and related fields.

Sign in / Sign up

Export Citation Format

Share Document