Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Estimates for radial solutions to the wave equation


Authors: Javier Duoandikoetxea, Adela Moyua and Osane Oruetxebarria
Journal: Proc. Amer. Math. Soc. 144 (2016), 1543-1552
MSC (2010): Primary 35L05; Secondary 35B05
DOI: https://doi.org/10.1090/proc/12767
Published electronically: December 21, 2015
MathSciNet review: 3451231
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We consider the Cauchy problem for the wave equation with null initial position and radial initial velocity $ \psi $. With the solution $ u$ of this problem we define the operator $ S(\psi )=\sup _{t>0}t^{-1}\vert u(x,t)\vert$. Using simple one-dimensional operators to bound pointwise the operator $ S$ we obtain weighted $ L^p$ estimates with power weights. Even for the unweighted estimates the result for dimension higher than 3 differs from the one with general functions.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 35L05, 35B05

Retrieve articles in all journals with MSC (2010): 35L05, 35B05


Additional Information

Javier Duoandikoetxea
Affiliation: Departamento de Matemáticas, Universidad del País Vasco/Euskal Herriko Unibertsitatea, Apartado 644, 48080 Bilbao, Spain
Email: javier.duoandikoetxea@ehu.eus

Adela Moyua
Affiliation: Departamento de Matemáticas, Universidad del País Vasco/Euskal Herriko Unibertsitatea, Apartado 644, 48080 Bilbao, Spain

Osane Oruetxebarria
Affiliation: Departamento de Matemáticas, Universidad del País Vasco/Euskal Herriko Unibertsitatea, Apartado 644, 48080 Bilbao, Spain
Email: osane.oruetxebarria@ehu.eus

DOI: https://doi.org/10.1090/proc/12767
Keywords: Wave equation, radial solutions, weighted inequalities
Received by editor(s): October 16, 2014
Received by editor(s) in revised form: February 25, 2015
Published electronically: December 21, 2015
Additional Notes: This work was supported by grant MTM2011-24054 of the Ministerio de Economía y Competitividad (Spain) and grant IT-641-13 of the Basque Gouvernment
Adela Moyua (1956-2013). The author passed away during the production of this work
Communicated by: Joachim Krieger
Article copyright: © Copyright 2015 American Mathematical Society

American Mathematical Society