Naslov
On a generalization of compensated compactness in the $L^p-L^q$ setting

Autori
Mišur, Marin ; Mitrović, Darko

Izvornik
Journal of functional analysis (0022-1236) 268 (2015), 7; 1904-1927

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
$L^p-L^q$ compensated compactness; H-distributions; non-strictly parabolic equations; weak convergence method

Sažetak
We investigate conditions under which, for two sequences $(\u_r)$ and $(\vv_r)$ weakly converging to $\u$ and $\vv$ in $L^p(\R^d ; \R^N)$ and $L^{; ; ; ; q}; ; ; ; (\R^d ; \R^N)$, respectively, $1/p+1/q \leq 1$, a quadratic form $q(\mx ; \u_r, \vv_r)=\sum\limits_{; ; ; ; j, m=1}; ; ; ; ^N q_{; ; ; ; j m}; ; ; ; (\mx)u_{; ; ; ; j r}; ; ; ; v_{; ; ; ; m r}; ; ; ; $ converges toward $q(\mx ; \u, \vv)$ in the sense of distributions. The conditions involve fractional derivatives and variable coefficients, and they represent a generalization of the known compensated compactness theory. The proofs are accomplished using a recently introduced $H$-distribution concept. We apply the developed techniques to a nonlinear (degenerate) parabolic equation.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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