Regularity of solutions of two-dimensional Monge-Ampère equations
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- by Friedmar Schulz and Liang Yuan Liao PDF
- Trans. Amer. Math. Soc. 307 (1988), 271-277 Request permission
Abstract:
In the paper we investigate the regularity of solutions $z(x, y) \in {C^{1,1}}(\Omega )$, resp. ${C^{1,1}}(\overline \Omega )$ of elliptic Monge-Ampére equations of the form \[ Ar + 2Bs + Ct + (rt - {s^2}) = E.\] It is shown that $z(x, y) \in {C^{2,\alpha }}(\Omega )$, resp. ${C^{2,\alpha }}(\overline \Omega )$, with corresponding a priori estimates, if $A, B, C, E \in {C^\alpha }(\Omega \times {{\mathbf {R}}^3})$. The results are deduced via the Campanato technique for equations of variational structure invoking a Legendre-like transformation.References
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Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 307 (1988), 271-277
- MSC: Primary 35J60; Secondary 35B65
- DOI: https://doi.org/10.1090/S0002-9947-1988-0936816-1
- MathSciNet review: 936816