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| Volume 7, Number 3, December 2006, pp. 541-551 | ||||||||
|
Richard L. Wheeden |
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| Key words: | ||||||||
| regularity, subelliptic equations, Hölder continuity, Monge-Ampère equations, partial Legendre transform. | ||||||||
| Mathematices Subject Classification: 35B65, 35B45, 35D10, 35H20. | ||||||||
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| Abstract: | |||
| The main results concern local Hölder continuity of the solutions of classes of subelliptic equations with rough coefficients, as well as an application to regularity results for degenerate Monge-Ampère equations. A connection between Monge-Amp?ere equations and those of subelliptic type is furnished by an n-dimensional partial Legendre transformation, which reduces the question of regularity for Monge-Ampère equations to a similar one for quasilinear equations. | |||
| Regularity results for some linear and nonlinear equations | ||