Abstract
This chapter develops a theory of second order linear elliptic equations that is essentially an extension of potential theory. It is based on the fundamental observation that equations with Hölder continuous coefficients can be treated locally as a perturbation of constant coefficient equations. From this fact Schauder [SC 4, 5] was able to construct a global theory, an extension of which is presented here. Basic to this approach are apriori estimates of solutions, extending those of potential theory to equations with Hölder continuous coefficients.
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© 1977 Springer-Verlag Berlin Heidelberg
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Gilbarg, D., Trudinger, N.S. (1977). Classical Solutions; the Schauder Approach. In: Elliptic Partial Differential Equations of Second Order. Grundlehren der mathematischen Wissenschaften, vol 224. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-96379-7_6
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DOI: https://doi.org/10.1007/978-3-642-96379-7_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-96381-0
Online ISBN: 978-3-642-96379-7
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