Summary
In this paper the exterior Dirichlet problem for linear elliptic equations in two independent variables with bounded measurable coefficients is investigated. An existence-uniqueness theorem is established in a suitably weighted Sobolev class. Some a-priori estimates are derived.
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A. D. Alexandrov,Majorization of solutions of second-order linear equations (in russian), Vestnik Leningrad. Univ.,21, no. 1 (1966), pp. 5–25; english version in A.M.S. Transl.,68 (1968), pp. 120–143.
A. D. Alexandrov,Majorants of solutions and uniqueness conditions for elliptic equations (in russian), Vestnik Leningrad. Univ.,21, no. 7 (1966), pp. 5–20; english version in A.M.S. Transl.,68 (1968), pp. 144–161.
S. Campi, Sul problema di Dirichlet esterno per equazioni lineari ellittiche in due variabili, Rend. Mat., 4,9 (VI) (1976), pp. 567–611.
N. Meyers -J. Serrin,The exterior Dirichlet problem for second order elliptic partial differential equations, J. Math. Mech.,9 (1960), pp. 513–538.
M. H. Protter -H. F. Weinberger,Maximum principles in differential equations, Prentice-Hall, Inc. Englewood Cliffs, N. J., 1967.
C. Pucci, Limitazioni per soluzioni di equazioni ellittiche, Ann. Mat. Pura Appl., 4,74 (1966), pp. 15–30.
G. Talenti,Equazioni lineari ellittiche in due variabili, Le Matematiche,21 (1966), pp. 339–376.
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Entrata in Redazione il 6 agosto 1977.
This research was supported by GNAFA-CNR.
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Campi, S. On the exterior dirichlet problem for linear elliptic equations in the plane. Annali di Matematica 119, 177–194 (1979). https://doi.org/10.1007/BF02413175
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DOI: https://doi.org/10.1007/BF02413175