Some counterexamples to the regularity of Monge-Ampère equations
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- by Xu Jia Wang
- Proc. Amer. Math. Soc. 123 (1995), 841-845
- DOI: https://doi.org/10.1090/S0002-9939-1995-1223269-0
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Abstract:
We present examples to show that the solution u of the Monge-Ampère equation $\det ({D^2}u) = f(x)$, with $u = 0$ on the boundary, may not lie in ${W^{2,p}}$ or in ${C^{1,\alpha }}$ for noncontinuous and positive $f(x)$ and for continuous and nonnegative $f(x)$.References
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- Luis A. Caffarelli, Interior $W^{2,p}$ estimates for solutions of the Monge-Ampère equation, Ann. of Math. (2) 131 (1990), no. 1, 135–150. MR 1038360, DOI 10.2307/1971510
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Bibliographic Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 841-845
- MSC: Primary 35B65; Secondary 35J60
- DOI: https://doi.org/10.1090/S0002-9939-1995-1223269-0
- MathSciNet review: 1223269