Regularizing properties of space-periodic layer heat potentials and applications to boundary value problems in periodic domains |
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Authors: | Paolo Luzzini |
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Institution: | Dipartimento di Matematica Tullio Levi-Civita, Università degli Studi di Padova, Padua, Italy |
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Abstract: | We introduce space-periodic layer heat potentials and we prove some regularizing properties in parabolic Schauder spaces defined on the boundary of infinite parabolic cylinders. Then, we show how to exploit these mapping properties for the space-periodic layer potentials in order to solve two initial-boundary value problems for the heat equation in an unbounded periodic domain. |
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Keywords: | heat equation integral equations method integral operators in parabolic Schauder spaces periodic domains space-periodic layer heat potentials |
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