On time-periodic solutions to parabolic boundary value problems

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.