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Smoothness in the Dini Space of a Single Layer Potential for a Parabolic System in the Plane

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We prove estimates in the Dini space for the second order spatial derivative of a vector parabolic single layer potential. We obtain estimates for higher order derivatives of solutions to… Click to show full abstract

We prove estimates in the Dini space for the second order spatial derivative of a vector parabolic single layer potential. We obtain estimates for higher order derivatives of solutions to initial-boundary-value problems for one-dimensional parabolic systems with Dini-continuous coefficients in a curvilinear domain with nonsmooth lateral boundary.

Keywords: single layer; smoothness dini; dini space; layer potential

Journal Title: Journal of Mathematical Sciences
Year Published: 2018

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