Timeline for $L^2$-de-Rham complex on Lipschitz domains has smooth harmonic forms?
Current License: CC BY-SA 3.0
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| May 8, 2012 at 19:08 | comment | added | timur | @Martin: The interior regularity can be shown by applying a general regularity theorem on elliptic operators, see e.g. Folland's PDE book. I don't know if it gives the best results, but I think McLean's book on strongly elliptic systems contains some discussions on regularity up to the boundary when the boundary is not smooth. | |
| May 8, 2012 at 17:24 | comment | added | shuhalo | @timur: Thanks for your reference to Taylor, which I learned about just yesterday. Still, in the refered section he assumes a smooth boundary from the beginning. Furthermore, how ellipticity of the Hodge Laplacian enforces regularity is not clear to me - in case you mean elliptic regularity, I am aware that the solutions for the Hodge-Laplacian with right-hand side in L^2 and, say, homogenous tangential boundary conditions may gain regularity between 1/2 and 1 for Lipschitz domains. Yet, I do not know how more regular data imply more regular solutions, as in the scalar case. | |
| May 8, 2012 at 3:20 | history | answered | timur | CC BY-SA 3.0 |