A Note on Some Properties of Unbounded Bilinear Forms Associated with Skew-Symmetric $$$L^q(\Omega)$$$-Matrices

P.I. Kogut

doi:10.15421/242407

A Note on Some Properties of Unbounded Bilinear Forms Associated with Skew-Symmetric $$$L^q(\Omega)$$$-Matrices

P.I. Kogut (Oles Honchar Dnipro National University), https://orcid.org/0000-0003-1593-0510

Abstract

We study the bilinear forms on the space of measurable $$$p$$$-integrable functions which are generated by skew-symmetric matrices with unbounded coefficients. We give an example showing that if a skew-symmetric matrix contains a locally unbounded $$$L^q$$$-elements, then the corresponding quadratic forms can be alternating. These questions are closely related to the existence issues of the Nuemann boundary value problem for $$$p$$$-Laplace elliptic equations with non-symmetric and locally unbounded anisotropic diffusion matrices.

Keywords

skew-symmetric matrix; unbounded bilinear form

MSC 2020

Pri 15A63, Sec 11E16, 11E39

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