Fully Nonlinear Elliptic Equations

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¡ Colloquium Publications - American Mathematical Society āĻŦāχ 43 ¡ American Mathematical Soc.
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āĻāχ āχ-āĻŦ⧁āϕ⧇āϰ āĻŦāĻŋāĻˇā§Ÿā§‡

The goal of the book is to extend classical regularity theorems for solutions of linear elliptic partial differential equations to the context of fully nonlinear elliptic equations. This class of equations often arises in control theory, optimization, and other applications. The authors give a detailed presentation of all the necessary techniques. Instead of treating these techniques in their greatest generality, they outline the key ideas and prove the results needed for developing the subsequent theory. Topics discussed in the book include the theory of viscosity solutions for nonlinear equations, the Alexandroff estimate and Krylov-Safonov Harnack-type inequality for viscosity solutions, uniqueness theory for viscosity solutions, Evans and Krylov regularity theory for convex fully nonlinear equations, and regularity theory for fully nonlinear equations with variable coefficients.

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āϏāĻŋāϰāĻŋāϜ āĻĒāĻĄāĻŧāĻž āϚāĻžāϞāĻŋā§Ÿā§‡ āϝāĻžāύ

Luis A. Caffarelli āĻāϰ āĻĨ⧇āϕ⧇ āφāϰ⧋

āĻāĻ•āχ āϧāϰāύ⧇āϰ āχ-āĻŦ⧁āĻ•