Auscher, P.; Tchamitchian, Ph. Estimates on Green’s kernel using wavelets and applications. (English) Zbl 0803.35154 Schumaker, Larry L. (ed.) et al., Recent advances in wavelet analysis. Boston, MA: Academic Press, Inc.. Wavelet Anal. Appl. 3, 63-86 (1994). Summary: We study some elliptic differential operators with non-smooth coefficients in dimension 1. The main idea is to construct an adapted wavelet basis to any given such operator so that its matrix in this basis enjoys nice fall-off properties away from the diagonal. Estimates on the inverse matrix are obtained, and lead to estimates on the Green’s kernel of the operator. An application is given to a square root problem for which we obtain Calderón-Zygmund estimates on the associated kernels.For the entire collection see [Zbl 0782.00090]. MSC: 35R05 PDEs with low regular coefficients and/or low regular data 42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems 34B27 Green’s functions for ordinary differential equations 65L10 Numerical solution of boundary value problems involving ordinary differential equations Keywords:elliptic differential operators with non-smooth coefficients in dimension 1; adapted wavelet basis; estimates on the Green’s kernel; square root problem; Calderón-Zygmund estimates PDFBibTeX XMLCite \textit{P. Auscher} and \textit{Ph. Tchamitchian}, Wavelet Anal. Appl. 3, 63--86 (1994; Zbl 0803.35154)