Nonvariational layer potentials with respect to H¨older continuous vector fields

Verchota, Gregory C.

doi:10.4171/RMI/491

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Revista Matemática Iberoamericana

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Volume 23, Issue 1, 2007, pp. 201–212

DOI: 10.4171/RMI/491

Published online: 2007-04-30

Nonvariational layer potentials with respect to H¨older continuous vector fields

Gregory C. Verchota^[1]

(1) Syracuse University, USA

Nontangential a.e. vanishing of the oblique derivative of a harmonic function with respect to a Hölder continuous vector field on a Lipschitz boundary is shown to imply that the harmonic function is constant.

Keywords: Oblique derivative, Lipschitz domain, uniqueness

Verchota Gregory: Nonvariational layer potentials with respect to H¨older continuous vector fields. Rev. Mat. Iberoam. 23 (2007), 201-212. doi: 10.4171/RMI/491