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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A note on the convergence to initial data of heat and Poisson equations


Authors: Silvia I. Hartzstein, José L. Torrea and Beatriz E. Viviani
Journal: Proc. Amer. Math. Soc. 141 (2013), 1323-1333
MSC (2010): Primary 42B99; Secondary 35G10
Published electronically: August 24, 2012
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Abstract: We characterize the weighted Lebesgue spaces, $ L^p(\mathbb{R}^n,v(x)dx),$ for which the solutions of the Heat and Poisson problems have limits a.e. when the time $ t$ tends to zero.


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Additional Information

Silvia I. Hartzstein
Affiliation: Facultad de Ingeniería Química, Universidad Nacional del Litoral e Instituto de Matemática Aplicada del Litoral, Conicet, Santa Fe, Argentina
Email: shartzstein@santafe-conicet.gov.ar

José L. Torrea
Affiliation: Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, 28049 Madrid, Spain — and — ICMAT CSIC-UAM-UCM-UC3M
Email: joseluis.torrea@uam.es

Beatriz E. Viviani
Affiliation: Facultad de Ingeniería Química, Universidad Nacional del Litoral e Instituto de Matemática Aplicada del Litoral, Conicet, Santa Fe, Argentina
Email: viviani@santafe-conicet.gov.ar

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11441-8
PII: S 0002-9939(2012)11441-8
Received by editor(s): September 10, 2010
Received by editor(s) in revised form: August 11, 2011
Published electronically: August 24, 2012
Additional Notes: The authors were partially supported by MTM2008-06621-C02-01. The first and third authors were partially supported by grants from CONICET and Universidad Nacional del Litoral, Argentina.
This research was begun during a stay of the first and third authors at the Departamento de Matemáticas of UAM, to which they are very grateful.
Communicated by: Richard Rochberg
Article copyright: © Copyright 2012 American Mathematical Society