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Duality principles for fully nonlinear elliptic equations. (English) Zbl 1237.35053

Rodrigues, José F. (ed.) et al., Trends in partial differential equations of mathematical physics. Selected papers of the international conference held on the occasion of the 70th birthday of V. A. Solonnikov, Óbidos, Portugal, June 7–10, 2003. Basel: Birkhäuser (ISBN 3-7643-7165-X/hbk). Progress in Nonlinear Differential Equations and their Applications 61, 125-136 (2005).
Summary: In this paper we use duality theory to associate certain measures to fully nonlinear elliptic equations. These measures are the natural extension of the Mather measures to controlled stochastic processes and associated second order elliptic equations. We apply these ideas to prove new a priori estimates for smooth solutions of fully nonlinear elliptic equations
For the entire collection see [Zbl 1062.35005].

MSC:

35J60 Nonlinear elliptic equations
37J50 Action-minimizing orbits and measures (MSC2010)
49N15 Duality theory (optimization)
35B45 A priori estimates in context of PDEs
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