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Time-periodic solutions to partial differential equations of parabolic typecorresponding to an operator that is elliptic in the sense ofAgmon-Douglis-Nirenberg are investigated. In the whole- and half-space case weconstruct an explicit formula for the solution and establish coercive Lpestimates. The estimates generalize a famous result of Agmon, Douglis andNirenberg for elliptic problems to the time-periodic case.

On Time-Periodic Solutions to Parabolic Boundary Value Problems of Agmon-Douglis-Nirenberg Type