Phase Space Analysis for the Heat Equation

Marcelo R. Ebert and Michael Reissig
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Marcelo R. Ebert: University of São Paulo, Department of Computing and Mathematics
Michael Reissig: TU Bergakademie Freiberg, Institute of Applied Analysis

Chapter Chapter 12 in Methods for Partial Differential Equations, 2018, pp 173-179 from Springer

Abstract: Abstract This chapter explains in an elementary way via the Cauchy problem for the heat equation without with and mass term how phase space analysis and interpolation techniques can be used to prove L p − L q estimates on and away from the conjugate line 1 p + 1 q = 1 $$\frac {1}{p}+\frac {1}{q}=1$$ , p ∈ [1, ∞]. Here we distinguish between L p − L q estimates for low regular and for large regular data.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-66456-9_12

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DOI: 10.1007/978-3-319-66456-9_12

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