Adjoint Methods for the Infinity Laplacian Partial Differential Equation |
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Authors: | Lawrence C Evans Charles K Smart |
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Institution: | 1. Department of Mathematics, University of California, Berkeley, USA
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Abstract: | To study fine properties of certain smooth approximations ${u^\varepsilon}$ to a viscosity solution u of the infinity Laplacian partial differential equation (PDE), we introduce Green??s function ${\sigma^\varepsilon}$ for the linearization. We can then integrate by parts with respect to ${\sigma^\varepsilon}$ and derive various useful integral estimates. We are, in particular, able to use these estimates (i) to prove the everywhere differentiability of u and (ii) to rigorously justify interpreting the infinity Laplacian equation as a parabolic PDE. |
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