A Survey on the Boundary Behavior of the Double Layer Potential in Schauder Spaces in the Frame of an Abstract Approach

Lanza de Cristoforis, Massimo

doi:10.1007/978-3-031-59591-2_6

Trends in Mathematics

2024

DOI: 10.1007/978-3-031-59591-2_6

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A Survey on the Boundary Behavior of the Double Layer Potential in Schauder Spaces in the Frame of an Abstract Approach

Massimo Lanza de Cristoforis

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2024

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Cited by 2 publications

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Continuity of the Double Layer Potential of a Second Order Elliptic Differential Operator in Schauder Spaces on the Boundary

Lanza de Cristoforis

2024

J Math Sci

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We prove the validity of a regularizing property on the boundary of the double layer potential associated with the fundamental solution of a nonhomogeneous second order elliptic differential operator with constant coefficients in Schauder spaces of exponent greater or equal to two that sharpens classical results of N.M. Günter, S. Mikhlin, V.D. Kupradze, T.G. Gegelia, M.O. Basheleishvili and T.V. Burchuladze, U. Heinemann and extends the work of A. Kirsch who has considered the case of the Helmholtz operator.

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Continuity of the Double Layer Potential of a Second Order Elliptic Differential Operator in Schauder Spaces on the Boundary

Lanza de Cristoforis

2024

J Math Sci

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A nonvariational form of the Neumann problem for the Poisson equation

Lanza de Cristoforis

2024

Complex Variables and Elliptic Equations

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A Survey on the Boundary Behavior of the Double Layer Potential in Schauder Spaces in the Frame of an Abstract Approach

Cited by 2 publications

References 34 publications

Continuity of the Double Layer Potential of a Second Order Elliptic Differential Operator in Schauder Spaces on the Boundary

Continuity of the Double Layer Potential of a Second Order Elliptic Differential Operator in Schauder Spaces on the Boundary

A nonvariational form of the Neumann problem for the Poisson equation

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