Question

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.?

Thanks for your help!

Answer 1

Have a look at Lunardi's book, it is more on the functional analytic questions you have:

http://books.google.co.uk/books/about/Analytic_semigroups_and_optimal_regulari.html?id=mWojiHzg9bEC

Answer 2

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,

D. D. Haroske and H. Triebel, Distributions, Sobolev spaces, elliptic equations, Zürich: European Mathematical Society, 2008;

N. V. Krylov, Lectures on elliptic and parabolic equations in Sobolev spaces, AMS, Providence, 2008.