Estimates for radial solutions to the wave equation
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- by Javier Duoandikoetxea, Adela Moyua and Osane Oruetxebarria PDF
- Proc. Amer. Math. Soc. 144 (2016), 1543-1552 Request permission
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 $S(\psi )=\sup _{t>0}t^{-1}|u(x,t)|$. 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
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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
- MR Author ID: 680066
- Email: osane.oruetxebarria@ehu.eus
- 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
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 1543-1552
- MSC (2010): Primary 35L05; Secondary 35B05
- DOI: https://doi.org/10.1090/proc/12767
- MathSciNet review: 3451231