A. A. Kovalevsky, “On the summability of entropy solutions for the Dirichlet problem in a class of non-linear elliptic fourth-order equations”, Izv. RAN. Ser. Mat., 2003, Volume 67, Issue 5,Pages <nobr>35

This article is cited in 11 papers

On the summability of entropy solutions for the Dirichlet problem in a class of non-linear elliptic fourth-order equations

A. A. Kovalevsky

Abstract: We present some results on the summability of entropy solutions for the Dirichlet problem in a class of fourth-order non-linear elliptic equations in relation to integrability properties of their right-hand sides. Consideration is given to the cases in which the right-hand sides belong to Lebesgue spaces with exponents close to unity and also to some wider sets contained in $L^1$.

UDC: 517.9

MSC: 35B45, 35D05, 35K60, 35R10

Received: 31.01.2001

DOI: 10.4213/im450