Abstract
This technique is exceedingly well suited to settle existence questions for boundary-value problems of elliptic differential equations under very weak hypotheses on the coefficients. Such techniques are necessary if we want to treat the existence problems for quasi-linear or still more general equations. The technique of Schauder is based on the use of exceedingly sharp a priori estimates for the solution.4 In Section III-1.4 we met the simplest such estimate, with which, however, not very much can be done. We outline the method in a presentation which is not too general and without giving the complete hypotheses. However, the precise proof will not be any simpler than the one given in Section IV-3.
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© 1964 Springer Fachmedien Wiesbaden
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Hellwig, G. (1964). Schauder’s Technique of Proof for Existence Problems in Elliptic Differential Equations. In: Partial Differential Equations. Mathematische Leitfäden. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-11002-6_17
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DOI: https://doi.org/10.1007/978-3-663-11002-6_17
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
Print ISBN: 978-3-519-12213-5
Online ISBN: 978-3-663-11002-6
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