most recent 30 from http://mathoverflow.net 2013-05-19T02:47:50Z http://mathoverflow.net/feeds/question/65317 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/65317/reference-for-neumann-laplacian Marc 2011-05-18T11:19:18Z 2011-10-18T22:13:58Z

<p>Let $\Omega\subset R^d$ be a bounded, smooth domain. Consider $A=-\Delta$ subject to homogeneous Neumann boundary conditions in $L^p$-spaces. Does anybody know a good reference book on basic results like closedness and semigroup properties etc.?</p> <p>Thanks for your help!</p>

http://mathoverflow.net/questions/65317/reference-for-neumann-laplacian/65329#65329 Anatoly Kochubei 2011-05-18T13:33:16Z 2011-05-18T13:33:16Z

<p>There are many books about the $L^p$-theory of elliptic and parabolic equations covering, in particular the case of the Neumann Laplacian. See, for example,</p> <p>D. D. Haroske and H. Triebel, Distributions, Sobolev spaces, elliptic equations, Zürich: European Mathematical Society, 2008;</p> <p>N. V. Krylov, Lectures on elliptic and parabolic equations in Sobolev spaces, AMS, Providence, 2008.</p>

http://mathoverflow.net/questions/65317/reference-for-neumann-laplacian/78495#78495 András Bátkai 2011-10-18T22:13:58Z 2011-10-18T22:13:58Z

<p>Have a look at Lunardi's book, it is more on the functional analytic questions you have:</p> <p><a href="http://books.google.co.uk/books/about/Analytic_semigroups_and_optimal_regulari.html?id=mWojiHzg9bEC" rel="nofollow">http://books.google.co.uk/books/about/Analytic_semigroups_and_optimal_regulari.html?id=mWojiHzg9bEC</a></p>