Second order linear parabolic equations in uniform spaces in \({\varvec{\mathbb {R}^{N}}}\)

Abstract

We solve second order parabolic equations with nonsmooth coefficients and initial data in suitable uniform spaces. We also show the smoothing effect of the corresponding analytic semigroup depending on the integrability properties of the coefficients. Robustness with respect to perturbations in the coefficients is also obtained.

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Correspondence to Aníbal Rodríguez-Bernal.

Additional information

Partially supported by Project MTM2012-31298, MICINN and GR58/08 Grupo 920894, UCM, Spain.

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Quesada, C., Rodríguez-Bernal, A. Second order linear parabolic equations in uniform spaces in \({\varvec{\mathbb {R}^{N}}}\) . Rev Mat Complut 30, 63–78 (2017). https://doi.org/10.1007/s13163-016-0215-0

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Keywords

  • Parabolic equations
  • Analytic semigroups
  • Perturbation
  • Smoothing
  • Uniform spaces

Mathematics Subject Classification

  • 35B20
  • 35B30
  • 35B35
  • 35B65
  • 35K10
  • 35K15
  • 47D03
  • 47D06