Nonhomogeneous Neumann problem for the Poisson equation in domains with an external cusp
In this work we analyze the existence and regularity of the solution of a nonhomogeneous Neumann problem for the Poisson equation in a plane domain Ω with an external cusp. In order to prove that there exists a unique solution in H1 (Ω) using the Lax-Milgram theorem we need to apply a trace theorem....
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| Autores principales: | , , , |
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| Formato: | JOUR |
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_0022247X_v310_n2_p397_Acosta |
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| Sumario: | In this work we analyze the existence and regularity of the solution of a nonhomogeneous Neumann problem for the Poisson equation in a plane domain Ω with an external cusp. In order to prove that there exists a unique solution in H1 (Ω) using the Lax-Milgram theorem we need to apply a trace theorem. Since Ω is not a Lipschitz domain, the standard trace theorem for H1 (Ω) does not apply, in fact the restriction of H1 (Ω) functions is not necessarily in L2 (∂Ω). So, we introduce a trace theorem by using weighted Sobolev norms in Ω. Under appropriate assumptions we prove that the solution of our problem is in H2 (Ω) and we obtain an a priori estimate for the second derivatives of the solution. © 2005 Elsevier Inc. All rights reserved. |
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