We study the Gamma-convergence, as p tends to +infinity, of the power-law functionals F-p(V) = (f Omega f(p) (x, V(x))dx)(1/p), in the setting of constant-rank operator A. We show that the Gamma-limit is given by a supremal functional on L infinity(Omega; M-dxN) boolean AND KerA, where M-dxN is the space of dxN real matrices. We give an explicit representation formula for the supremand function. We provide some examples and as an application of the Gamma-convergence results we characterize the strength set in the context of electrical resistivity.
POWER-LAW APPROXIMATION UNDER DIFFERENTIAL CONSTRAINTS / Ansini, Nadia; Francesca, Prinari. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - ELETTRONICO. - 46:2(2014), pp. 1085-1115. [10.1137/130911391]
POWER-LAW APPROXIMATION UNDER DIFFERENTIAL CONSTRAINTS
ANSINI, NADIA;
2014
Abstract
We study the Gamma-convergence, as p tends to +infinity, of the power-law functionals F-p(V) = (f Omega f(p) (x, V(x))dx)(1/p), in the setting of constant-rank operator A. We show that the Gamma-limit is given by a supremal functional on L infinity(Omega; M-dxN) boolean AND KerA, where M-dxN is the space of dxN real matrices. We give an explicit representation formula for the supremand function. We provide some examples and as an application of the Gamma-convergence results we characterize the strength set in the context of electrical resistivity.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.