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dc.contributor.authorKovats, Jay
dc.date.accessioned2015-04-10T15:29:41Z
dc.date.available2015-04-10T15:29:41Z
dc.date.issued1999-09-25
dc.identifier.citationKovats, J. (1999) Dini-Campanato spaces and applications to nonlinear elliptic equations. Electronic Journal of Differential Equations, 1999(37), 1-20.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttp://hdl.handle.net/11141/552
dc.description.abstractWe generalize a result due to Campanato [C] and use this to obtain regularity results for classical solutions of fully nonlinear elliptic equations. We demonstrate this technique in two settings. First, in the simplest setting of Poisson's equation Delta u=f in B, where f is Dini continuous in B, we obtain known estimates on the modulus of continuity of second derivatives D2u in a way that does not depend on either differentiating the equation or appealing to integral representations of solutions. Second, we use this result in the concave, fully nonlinear setting F(D^2u,x)=f(x) to obtain estimates on the modulus of continuity of D^2u when the L^n averages of f satisfy the Dini condition.en_US
dc.language.isoen_USen_US
dc.rightsThis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.en_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc/3.0/en_US
dc.titleDini-Campanato spaces and applications to nonlinear elliptic equationsen_US
dc.typeArticleen_US


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This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Except where otherwise noted, this item's license is described as This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.