Application of Serrin’s kernel parametrix to the uniqueness of 𝐿₁ solutions of elliptic equations in the unit ball

Diederich, J. R.

doi:10.1090/S0002-9939-1975-0355308-0

Application of Serrin’s kernel parametrix to the uniqueness of $L_1$ solutions of elliptic equations in the unit ball
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by J. R. Diederich PDF

Proc. Amer. Math. Soc. 47 (1975), 341-347 Request permission

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.

References

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