The Neumann problem and Helmholtz decomposition in convex domains |
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| Authors: | Jun Geng |
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| Affiliation: | Department of Mathematics, University of Kentucky, Lexington, KY 40506, United States |
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| Abstract: | We show that the Neumann problem for Laplace's equation in a convex domain Ω with boundary data in Lp(∂Ω) is uniquely solvable for 1<p<∞. As a consequence, we obtain the Helmholtz decomposition of vector fields in Lp(Ω,Rd). |
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| Keywords: | Neumann problem Convex domains Helmholtz decomposition |
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