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Application of Serrin's kernel parametrix to the uniqueness of $ L_1$ solutions of elliptic equations in the unit ball


Author: J. R. Diederich
Journal: Proc. Amer. Math. Soc. 47 (1975), 341-347
MSC: Primary 35J15
DOI: https://doi.org/10.1090/S0002-9939-1975-0355308-0
MathSciNet review: 0355308
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Abstract: In this paper it will be established that $ {L_1}$ solutions of elliptic partial differential equations, with $ \alpha $-Hölder continuous coefficients, which assume their boundary values mean continuously on the boundary of the $ N$-dimensional unit ball are uniquely determined. An additional application of the kernel will be to establish the Fatou radial limit theorem.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0355308-0
Keywords: Second order elliptic, uniqueness, mean continuity, radial limit
Article copyright: © Copyright 1975 American Mathematical Society

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