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arXiv · 1901.08631

A comparison theorem for nonsmooth nonlinear operators

Vladimir Kozlov·Alexander Nazarov
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Abstract

We prove a comparison theorem for super- and sub-solutions with non-vanishing gradients to semilinear PDEs provided a nonlinearity $f$ is $L^p$ function with $p > 1$. The proof is based on a strong maximum principle for solutions of divergence type elliptic equations with VMO leading coefficients and with lower order coefficients from a Kato class. An application to estimation of periodic water waves profiles is given.

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Vladimir Kozlov, Alexander Nazarov. 2019-01-24. A comparison theorem for nonsmooth nonlinear operators. https://arxiv.org/abs/1901.08631

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