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Lp-theory of boundary integral equations on a contour with outward peak

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Abstract

A boundary integral equations of the second kind in the logarithmic potential theory are studied under the assumption that the contour has a peak. For each equation we find a pair of function spaces such that the corresponding operator map one of them onto another. We describe also the kernels of the operators and find a condition for the triviality of these kernels.

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Maz'ya, V., Soloviev, A. Lp-theory of boundary integral equations on a contour with outward peak. Integr equ oper theory 32, 75–100 (1998). https://doi.org/10.1007/BF01193508

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