Conjecture de Kato sur les ouverts de $\mathbb R$

Pascal Auscher, Philippe Tchamitchian

Type: Article

Publication Date: 1992-08-31

Citations: 14

DOI: https://doi.org/10.4171/rmi/121

Abstract

We prove Kato's conjecture for second order elliptic differential operators on an open set in dimension 1 with arbitrary boundary conditions. The general case reduces to studying the operator T = –\frac{d}{dx}a(x)\frac{d}{dx} on an interval, when a(x) is a bounded and accretive function. We show for the latter situation that the domain of T is spanned by an unconditional basis of wavelets with cancellation properties that compensate the action of the non-regular function a( x) .

Locations

Revista Matemática Iberoamericana - View - PDF

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