arXiv:2306.06497 Abstract | arXiv Analytics

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Applications of P-functions to Quasi-Linear equations: Gradient Bounds and Liouville-type properties

Published 2023-06-10Version 1

We introduce the notion of $ P -$functions for fully-nonlinear equations and obtain some abstract consequences. We study $ P- $functions for a class of quasi-linear equations and establish some general criterion for obtaining such quantities. Some applications are gradient bounds, De Giorgi-type properties of entire solutions and Liouville-type theorems. As a special case we obtain a gradient bound that differs from the Modica inequality. In addition, we provide examples of such quantities for the Monge-Ampere and for higher order nonlinear equations. One application for equations of order greater than two is pointwise estimates for the Laplacian.

Categories: math.AP

Keywords: gradient bound, quasi-linear equations, liouville-type properties, application, higher order nonlinear equations

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