Notes on the Infinity Laplace Equation

DOI10.1007/978-3-319-31532-4zbMATH Open1352.35045arXiv1411.1278OpenAlexW2269560399MaRDI QIDQ2798418

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Publication date: 12 April 2016

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Abstract: These notes are written up after my lectures at the University of Pittsburgh in March 2014 and at Tsinghua University in May 2014. My objective is the $infty$-Laplace Equation, a marvellous kin to the ordinary Laplace Equation. The $infty$-Laplace Equation has delightful counterparts to the Dirichlet integral, the Mean Value Theorem, the Brownian Motion, Harnack's Inequality and so on. It has applications to image processing and to mass transfer problems and provides optimal Lipschitz extensions of boundary values. My treaty of this "fully non-linear" degenerate equation is far from complete and generalizations are deliberately avoided.

Full work available at URL: https://arxiv.org/abs/1411.1278

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