ON SOME PROPERTIES OF UNBOUNDED BILINEAR FORMS ASSOCIATED WITH SKEW-SYMMETRIC L2(Ω)-MATRICES

Abstract

We study the bilinear forms on the space of measurable square-integrable functionswhich are generated by skew-symmetric matrices with unbounded coecients.We show that in the case when a skew-symmetric matrix contains L2-elements, the corresponding quadratic forms can be alternative. Since these questions are closely related with the existence of a unique solution for linear elliptic equations with unbounded coecients, we show that the energy identities for weak solutions can be studied in the framework of the corresponding alternative quadratic forms. To this end, we discuss the problems of integration by parts for measurable functions and give a generalization of some formulae for the non-Lipschitz case.

Keywords

• skew-symmetric matrices
• positive dened matrices
• unbounded bilinear form
• formula integration by parts
• Lipschitz functions