# On time-periodic solutions to parabolic boundary value problems

Mathematische Annalen, Jul 2018

Time-periodic solutions to partial differential equations of parabolic type corresponding to an operator that is elliptic in the sense of Agmon–Douglis–Nirenberg are investigated. In the whole- and half-space case we construct an explicit formula for the solution and establish coercive $$L^{p}$$ estimates. The estimates generalize a famous result of Agmon, Douglis and Nirenberg for elliptic problems to the time-periodic case.

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Mads Kyed, Jonas Sauer. On time-periodic solutions to parabolic boundary value problems, Mathematische Annalen, 2018, 1-29, DOI: 10.1007/s00208-018-1721-9