Abstract
We establish the existence and uniqueness of solutions of fully nonlinear elliptic second-order equations like H(v, Dv, D2v, x) = 0 in smooth domains without requiring H to be convex or concave with respect to the second-order derivatives. Apart from ellipticity nothing is required of H at points at which {pipe}D2v{pipe} ≤K, where K is any given constant. For large {pipe}D2v{pipe} some kind of relaxed convexity assumption with respect to D2v mixed with a VMO condition with respect to x are still imposed. The solutions are sought in Sobolev classes.
Original language | English (US) |
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Pages (from-to) | 687-710 |
Number of pages | 24 |
Journal | Communications in Partial Differential Equations |
Volume | 38 |
Issue number | 4 |
DOIs | |
State | Published - Apr 2013 |
Bibliographical note
Funding Information:The author was partially supported by NSF Grant DMS-1160569.
Keywords
- Bellman's equations
- Finite differences
- Fully nonlinear elliptic equations