On the existence of maximizers for a family of restriction theorems

Luca Fanelli, Luis Vega, Nicola Visciglia

Type: Article

Publication Date: 2011-03-22

Citations: 49

DOI: https://doi.org/10.1112/blms/bdr014

Abstract

We prove the existence of maximizers for a general family of restriction operators, up to the end-point. We also provide some counterxamples in the end-point case.

Locations

Bulletin of the London Mathematical Society - View
arXiv (Cornell University) - View - PDF
DataCite API - View

Similar Works

Action	Title	Year	Authors
+	Limits of Almost-Minimizers	2006
+	A simple proof of the maximum principle with endpoint constraints	2014	Adam Korytowski
+	An existence result for maximizations with respect to cones	1980	H. W. Corley
+	On a certain extension of the maximum principle	1963	Rudolf Výborný
+	6 The Zero Maximum Principle for Dual Monotonicity Cones	2023	Kevin R. Payne F. Reese Harvey H. Blaine Lawson
+	Local boundedness of minimizers in a limit case	1990	Nicola Fusco Carlo Sbordone
+	ON A MIN-MAX THEOREM	1997	Chen Fangqi
+	Maximum theorems with strict quasi-concavity and applications	2005	W.K. Kim K.H. Lee Ju Han Yoon
+	The Zero Maximum Principle for Dual Monotonicity Cones	2023
+	From an abstract maximal element principle to optimization problems, stationary point theorems and common fixed point theorems	2009	Lai-Jiu Lin Wei–Shih Du
+ PDF Chat	Some Minimax Theorems.	1972	Frode Terkelsen
+	Minimax theorems for ϕ−convex functions with applications	2014	Ewa M. Bednarczuk Monika Syga
+	Local Boundedness of Minimizers with Limit Growth Conditions	2015	Giovanni Cupini Paolo Marcellini Elvira Mascolo
+	Shorter Notes: The Minimax Principle and Uniqueness of the Friedrichs Extension	1969	Ebbe Thue Poulsen
+ PDF Chat	On the extended maximum principle	1964	Rudolf Výborný
+	Minimization Problems and Fixed Point Theorems	2019
+	A note on the strong maximum principle	2015	Michiel Bertsch Flavia Smarrazzo Alberto Tesei
+	A fixed point theorem for convex and decreasing operators	2005	Ke Li Jin Liang Ti‐Jun Xiao
+	Regularity Theorems and Maximum Principles	2013	Dumitru Motreanu V. V. Motreanu Nikolaos S. Papageorgiou
+	AN EXTENDED MAXIMUM PRINCIPLE	1997	Urszula Ledzewicz Heinz Schättler

Works That Cite This (48)

Action	Title	Year	Authors
+ PDF Chat	Optimal constants and extremisers for some smoothing estimates	2017	Neal Bez Mitsuru Sugimoto
+ PDF Chat	Minimizers for the fractional Sobolev inequality on domains	2018	Rupert L. Frank Tianling Jin Jingang Xiong
+ PDF Chat	Some Sharp Restriction Inequalities on the Sphere	2014	Emanuel Carneiro Diogo Oliveira e Silva
+	Minimizers for the fractional Sobolev inequality on domains	2017	Rupert L. Frank Tianling Jin Jingang Xiong
+	Sharp mixed norm spherical restriction	2018	Emanuel Carneiro Diogo Oliveira e Silva Mateus Sousa
+ PDF Chat	Global maximizers for adjoint Fourier restriction inequalities on low dimensional spheres	2020	Diogo Oliveira e Silva René Quilodrán
+	Existence of maximizers for Sobolev–Strichartz inequalities	2011	Luca Fanelli Luis Vega Nicola Visciglia
+	On existence of extremizers for the Tomas–Stein inequality for S1	2016	Shuanglin Shao
+ PDF Chat	Existence of extremals for a Fourier restriction inequality	2012	Francis Michael Christ Shuanglin Shao
+	A refinement of the Strichartz inequality with applications to the linear and nonlinear wave equations	2012	Javier Ramos Maravall

Works Cited by This (7)

Action	Title	Year	Authors
+	Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities	2002	Élliott H. Lieb
+ PDF Chat	A relation between pointwise convergence of functions and convergence of functionals	1983	Haı̈m Brezis Élliott H. Lieb
+	Existence of Extremals for a Fourier Restriction Inequality	2010	Michael Christ Shuanglin Shao
+ PDF Chat	Maximizers for the Strichartz Inequality	2007	Damiano Foschi
+ PDF Chat	Existence of extremals for a Fourier restriction inequality	2012	Francis Michael Christ Shuanglin Shao
+	Sharp Constants in the Hardy-Littlewood-Sobolev and Related Inequalities	1983	Élliott H. Lieb
+	A Relation Between Pointwise Convergence of Functions and Convergence of Functionals	1983	Haı̈m Brezis Élliott H. Lieb