Inverse positivity for general Robin problems on Lipschitz domains

Daniel Daners
Preprint (PDF) June 2008
Archiv der Mathematik, 92 (2009), 57 - 69
Original article at doi:10.1007/s00013-008-2918-z
Citations on Google Scholar


It is proved that elliptic boundary value problems in divergence form can be written in many equivalent forms. This is used to prove regularity properties and maximum principles for problems with Robin boundary conditions with negative or indefinite boundary coefficient on Lipschitz domains by rewriting them as a problem with positive coefficient. It is also shown that such methods cannot be applied to domains with an outward pointing cusp. Applications to the regularity of the harmonic Steklov eigenfunctions on Lipschitz domains are given.

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AMS Subject Classification (2000): 35J25 (35B50, 35B65)