Relaxation of a Quadratic Functional Defined by a Nonnegative Unbounded Matrix |
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Authors: | Casado-díaz Juan |
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Institution: | (1) Departamento de Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, C. Tarfía s/n, 41012 Sevilla, Spain. e-mail |
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Abstract: | We study the lower semicontinuous envelope in Lp(), F, of a functional F of the form F(u)=A uudx where A=A(x) is not strictly elliptic and not bounded. We prove that F; may also be written as F;(u)= Buudx with B=AP A for a matrix P which is the matrix of an orthogonal projection. In the one-dimensional case, we characterize the domain of F and we explicit the matrix P. |
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Keywords: | Relaxation lower semicontinuity |
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