Regularity of solutions of the Neumann problem for the Laplace equation
<p>Let <em>u</em> be a solution of the Neumann problem for the Laplace equation in <em>G</em> with the boundary condition <em>g</em>. It is shown that <em>u</em> ∈ <em>L</em> <em><sup>q</sup></em> (∂ <em&g...
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| Format: | Article |
| Language: | English |
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Università degli Studi di Catania
2006-11-01
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| Series: | Le Matematiche |
| Online Access: | http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/121 |
| Summary: | <p>Let <em>u</em> be a solution of the Neumann problem for the Laplace equation in <em>G</em> with the boundary condition <em>g</em>. It is shown that <em>u</em> ∈ <em>L</em> <em><sup>q</sup></em> (∂ <em>G</em> ) (equivalently, <em>u</em> ∈ <em>B<sup>q,2</sup><sub>1/q</sub></em> (<em>G</em> ) for <em>1 < q ≤ 2</em>, <em>u</em> ∈ <em>L<sup>q</sup> <sub>1/q</sub> (G ) </em>for <em>2 ≤ q < ∞</em>) if and only if the single layer potential corresponding to the boundary condition <em>g</em> is in <em>L <sup>q</sup> (∂ G )</em>. As a consequence we give a regularity result for some nonlinear boundary value problem.</p> |
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| ISSN: | 0373-3505 2037-5298 |