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We prove quadratic estimates for complex perturbations of Diractype operators, and thereby show that such operators have a bounded functional calculus. As an application we show that spectral… (More)

We survey some results concerning Cli ord analysis and the L theory of boundary value problems on domains with Lipschitz boundaries. Some novelty is introduced when using Rellich inequalities to… (More)

We consider second order elliptic divergence form systems with complex measurable coefficients A that are independent of the transversal coordinate, and prove that the set of A for which the boundary… (More)

- Pascal Auscher, Angela Hahn Axelsson, Alan Mcintosh
- 2009

We provide a direct proof of a quadratic estimate that plays a central role in the determination of domains of square roots of elliptic operators and, as shown more recently, in some boundary value… (More)

- PASCAL AUSCHER, Angela Hahn Axelsson, Steve Hofmann
- 2007

We prove that the Neumann, Dirichlet and regularity problems for divergence form elliptic equations in the half space are well posed in L2 for small complex L∞ perturbations of a coefficient matrix… (More)

We solve the Kato square root problem for second order elliptic systems in divergence form under mixed boundary conditions on Lipschitz domains. This answers a question posed by J.-L. Lions in 1962.… (More)

- Manuel Alfonseca, PASCAL AUSCHER, Angela Hahn Axelsson, Steve Hofmann, Seick Kim
- 2010

A. We consider divergence form elliptic operators of the form L = − div A(x)∇, defined in Rn+1 = {(x, t) ∈ Rn × R}, n ≥ 2, where the L∞ coefficient matrix A is (n + 1) × (n + 1), uniformly… (More)

- PASCAL AUSCHER, Angela Hahn Axelsson
- 2009

We prove weighted estimates for the maximal regularity operator. Such estimates were motivated by boundary value problems. We take this opportunity to study a class of weak solutions to the abstract… (More)

The numerical solution of initial value problems in ordinary differential equations by means of boundary value techniques is considered. We discuss a finite-difference method which was already… (More)

- Manuel Alfonseca, PASCAL AUSCHER, Angela Hahn Axelsson, Steve Hofmann, Seick Kim
- 2008

A. We consider divergence form elliptic operators of the form L = −div A(x)∇, defined inRn+1 = {(x, t) ∈ Rn × R}, n ≥ 2, where theL∞ coefficient matrixA is (n + 1) × (n + 1), uniformly… (More)