Dini-Campanato Spaces and Applications to Nonlinear Elliptic Equations
Date
1999-09-25
Authors
Kovats, Jay
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
We 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 = ƒ in B, where ƒ 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) = ƒ(x) to obtain estimates on the modulus of continuity of D2u when the Ln averages of ƒ satisfy the Dini condition.
Description
Keywords
Fully nonlinear elliptic equations, Polynomial approximation, Dini condition
Citation
Kovats, J. (1999). Dini-Campanato spaces and applications to nonlinear elliptic equations. <i>Electronic Journal of Differential Equations, 1999</i>(37), pp. 1-20.
Rights
Attribution 4.0 International
Rights Holder
This work is licensed under a Creative Commons Attribution 4.0 International License.