Abstract
In this paper we answer a question posed by E. Sanchez-Palencia which arose in the theory of homogenization of differential operators. The asymptotic behavior of solutions at infinity which have finite Dirichlet integral is studied and uniqueness theorems are also proved for exterior boundary problems for second-order elliptic equations in divergent form.
Similar content being viewed by others
Literature cited
V. A. Kondrat'ev and O. A. Oleinik, “Uniqueness theorems for solutions of exterior boundary problems and analogs of the St.-Venant principle,” Usp. Mat. Nauk,39, No. 4, 165–166 (1984).
G. H. Hardy, J. E. Littlewood, and G. Polya, Inequalities, Cambridge Univ. Press (1946).
E. De Georgi, “Sulla differentiabilita e l'analiticita della estremali degli integrali multipli regolare,” Mem. Sci. Torino,3, 1–19 (1957).
J. Moser, “A new proof of De Georgi's theorem concerning the regularity problem for elliptic differential equations,” Commun. Pure Appl. Math.,13, No. 13, 457–468 (1960).
W. Littman, G. Stampacchia, and G. F. Weinberger, “Regular points for elliptic equations with discontinuous coefficients,” Matematika (a collection of translations),9, No. 2, 72–97 (1965).
Additional information
Translated from Trudy Seminara im. I. G. Petrovskogo, No. 12, pp. 149–163, 1987.
Rights and permissions
About this article
Cite this article
Kondrat'ev, V.A., Oleinik, O.A. Asymptotics in a neighborhood of infinity of solutions with finite Dirichlet integral of second-order elliptic equations. J Math Sci 47, 2596–2607 (1989). https://doi.org/10.1007/BF01105913
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01105913