zbMATH — the first resource for mathematics

$$L^ p$$-regularity for systems of PDE’s, with coefficients in VMO. (English) Zbl 0830.35017
Krbec, Miroslav (ed.) et al., Nonlinear analysis, function spaces and applications. Vol. 5. Proceedings of the spring school held in Prague, May 23-28, 1994. Prague: Prometheus Publishing House. 1-32 (1994).
From the author’s introduction: “The purpose of these lectures is to review some recent work on the $$L^p$$ regularity of the maximum order derivatives of the solutions to a certain class of linear elliptic systems both in divergence and non divergence form with discontinuous coefficients. Here we shall see that the relevant assumption is that the coefficients belong to what is generally known as the space VMO. Recall that VMO consists of BMO functions whose integral oscillation over balls shrinking to a point converge uniformly to zero”.
For the entire collection see [Zbl 0811.00017].
Reviewer: M.Chicco (Genova)

MSC:
 35B65 Smoothness and regularity of solutions to PDEs 35J45 Systems of elliptic equations, general (MSC2000)
Full Text: