Singular Integral Neumann Boundary Conditions for Semilinear Elliptic PDEs
Keyword(s):
In this article, we discuss semilinear elliptic partial differential equations with singular integral Neumann boundary conditions. Such boundary value problems occur in applications as mathematical models of nonlocal interaction between interior points and boundary points. Particularly, we are interested in the uniqueness of solutions to such problems. For the sublinear and subcritical case, we calculate, on the one hand, illustrative, rather explicit solutions in the one-dimensional case. On the other hand, we prove in the general case the existence and—via the strong solution of an integro-PDE with a kind of fractional divergence as a lower order term—uniqueness up to a constant.
2018 ◽
Vol 145
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pp. 01009
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Analyzing and visualizing a discretized semilinear elliptic problem with Neumann boundary conditions
2002 ◽
Vol 18
(3)
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pp. 261-279
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1992 ◽
Vol 122
(1-2)
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pp. 137-160
2012 ◽
Vol 2012
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pp. 1-16
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