The Neumann problem on Lipschitz domains. (English) Zbl 0471.35026


35J25 Boundary value problems for second-order elliptic equations
31B20 Boundary value and inverse problems for harmonic functions in higher dimensions
26B20 Integral formulas of real functions of several variables (Stokes, Gauss, Green, etc.)
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
Full Text: DOI


[1] A. P. Calderon, C. P. Calderon, E. Fabes, M. Jodeit, and N. M. Rivière, Applications of the Cauchy integral on Lipschitz curves, Bull. Amer. Math. Soc. 84 (1978), no. 2, 287 – 290. · Zbl 0389.30025
[2] Björn E. J. Dahlberg, Estimates of harmonic measure, Arch. Rational Mech. Anal. 65 (1977), no. 3, 275 – 288. · Zbl 0406.28009 · doi:10.1007/BF00280445
[3] Björn E. J. Dahlberg, Weighted norm inequalities for the Lusin area integral and the nontangential maximal functions for functions harmonic in a Lipschitz domain, Studia Math. 67 (1980), no. 3, 297 – 314. · Zbl 0449.31002
[4] David S. Jerison and Carlos E. Kenig, An identity with applications to harmonic measure, Bull. Amer. Math. Soc. (N.S.) 2 (1980), no. 3, 447 – 451. · Zbl 0436.31002
[5] D. S. Jerison and C. E. Kenig, The Dirichlet problem in non-smooth domains, Ann. of Math. (to appear). · Zbl 0434.35027
[6] L. E. Payne and H. F. Weinberger, New bounds in harmonic and biharmonic problems, J. Math. and Phys. 33 (1955), 291 – 307. · Zbl 0064.09903 · doi:10.1002/sapm1954331291
[7] Franz Rellich, Darstellung der Eigenwerte von \Delta \?+\?\?=0 durch ein Randintegral, Math. Z. 46 (1940), 635 – 636 (German). · Zbl 0023.04204 · doi:10.1007/BF01181459
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.