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Schauder estimates and existence theory for entire solutions of linear elliptic equations

Published online by Cambridge University Press:  14 November 2011

Heinrich Begehr  and
G.N. Hile
Heinrich Begehr
Affiliation:
Institut für Mathematik I, Freie Universität Berlin, Arnimallee 3, D-1000 Berlin 33, West Germany
G.N. Hile
Affiliation:
Department of Mathematics, University of Hawaii, 2565 The Mall, Honolulu, Hawaii 96822, U.S.A.
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Synopsis

Existence as well as uniqueness theorems under certain growth conditions are given for entire solutions to linear elliptic equations in the n-dimensional space (2≦n). Introducing a proper norm, the proofs are based on a priori estimates. These estimates could be used to solve nonlinear equationsin the space, but the conditions on the nonlinearity have to be strong as the a priori estimates applyonly to classical, not to weak, solutions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 110 , Issue 1-2 , 1988 , pp. 101 - 123
Copyright
Copyright © Royal Society of Edinburgh 1988

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