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dc.contributor.authorKovats, Jay ( )
dc.date.accessioned2019-11-21T21:09:28Z
dc.date.available2019-11-21T21:09:28Z
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), pp. 1-20.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/8865
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 Δu = 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(D2u,x)=f(x) to obtain estimates on the modulus of continuity of D2u when the Ln averages of f satisfy the Dini condition.en_US
dc.formatText
dc.format.extent20 pages
dc.format.medium1 file (.pdf)
dc.language.isoen_USen_US
dc.publisherTexas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 1999, San Marcos, Texas: Southwest Texas State University and University of North Texas.
dc.subjectFully nonlinear elliptic equationsen_US
dc.subjectPolynomial approximationen_US
dc.subjectDini conditionen_US
dc.titleDini-Campanato Spaces and Applications to Nonlinear Elliptic Equationsen_US
txstate.documenttypeArticle
dc.rights.licenseCreative Commons Attribution 4.0 International License https://creativecommons.org/licenses/by/4.0/


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