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Some Counterexamples to the Regularity of Monge-Ampère Equations

Xu-Jia Wang
Proceedings of the American Mathematical Society
Vol. 123, No. 3 (Mar., 1995), pp. 841-845
DOI: 10.2307/2160809
Stable URL: http://www.jstor.org/stable/2160809
Page Count: 5
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Some Counterexamples to the Regularity of Monge-Ampère Equations
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Abstract

We present examples to show that the solution u of the Monge-Ampère equation $\det(D^2u) = f(x)$, with u = 0 on the boundary, may not lie in W2, p or in C1, α for noncontinuous and positive f(x) and for continuous and nonnegative f(x).

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