A note on the convergence to initial data of heat and Poisson equations
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- by Silvia I. Hartzstein, José L. Torrea and Beatriz E. Viviani PDF
- Proc. Amer. Math. Soc. 141 (2013), 1323-1333 Request permission
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.References
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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
- 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
- © Copyright 2012 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 141 (2013), 1323-1333
- MSC (2010): Primary 42B99; Secondary 35G10
- DOI: https://doi.org/10.1090/S0002-9939-2012-11441-8
- MathSciNet review: 3008879