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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Second-order equations of fixed type in regions with corners. I

Author: Leonard Sarason
Journal: Trans. Amer. Math. Soc. 261 (1980), 387-416
MSC: Primary 35G15; Secondary 35J25, 35K20, 35L20
MathSciNet review: 580895
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Abstract | References | Similar Articles | Additional Information

Abstract: A class of well-posed boundary value problems for second order equations in regions with corners and edges is studied. The boundary condition may involve oblique derivatives, and edge values may enter the graph of the associated Hilbert space operator. Uniqueness of weak solutions and existence of strong solutions is shown.

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  • [1] S. Agmon, A. Douglis, and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I, Comm. Pure Appl. Math. 12 (1959), 623–727. MR 0125307 (23 #A2610)
  • [2] R. Courant and D. Hubert, Methods of mathematical physics, Vol. II, Interscience, New York, 1962.
  • [3] J.-L. Lions and E. Magenes, Non-homogeneous boundary value problems and applications. Vol. I, Springer-Verlag, New York-Heidelberg, 1972. Translated from the French by P. Kenneth; Die Grundlehren der mathematischen Wissenschaften, Band 181. MR 0350177 (50 #2670)
  • [4] R. S. Phillips and Leonard Sarason, Elliptic-parabolic equations of the second order, J. Math. Mech. 17 (1967/1968), 891–917. MR 0219868 (36 #2942)
  • [5] L. Sarason, Second order equations of fixed typed in regions with corners. II (in preparation).

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PII: S 0002-9947(1980)0580895-3
Article copyright: © Copyright 1980 American Mathematical Society

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