A Liouville comparison principle for solutions of semilinear elliptic second-order partial differential inequalities

Vasilii V. Kurta

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arXiv · 2106.08866

A Liouville comparison principle for solutions of semilinear elliptic second-order partial differential inequalities

Vasilii V. Kurta

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Abstract

We consider semilinear elliptic second-order partial differential inequalities of the form Lu +|u|q-1u < and = Lv +|v|q-1v (*) in the whole space Rn, where n > and = 2, q > 0 and L is a linear elliptic second-order partial differential operator in divergence form. We assume that the coefficients of the operator L are defined, measurable and locally bounded in Rn, and that the quadratic form associated with the operator L is symmetric and non-negative definite. We obtain a Liouville comparison principle in terms of a capacity associated with the operator L for solutions of (*), which are defined and measurable in Rn and which belong locally to a Sobolev-type function space also associated with the operator L.

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Vasilii V. Kurta. 2021-06-16. A Liouville comparison principle for solutions of semilinear elliptic second-order partial differential inequalities. https://arxiv.org/abs/2106.08866

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