On Hofmann's bilinear estimate
Pascal Auscher (LM-Orsay)
TL;DR
This paper extends bilinear estimates and domain identification criteria for weak solutions of symmetric systems, building on Hofmann's work and previous results for Laplace's equation on Lipschitz domains.
Contribution
It generalizes Hofmann's bilinear estimate and domain criteria to systems, expanding their applicability beyond scalar equations.
Findings
Extended bilinear estimate for systems of equations.
Provided a criterion to identify the generator domain of the associated semi-group.
Built upon and generalized previous results for Laplace's equation.
Abstract
Using the framework of a previous article joint with Axelsson and McIntosh, we extend to systems two results of S. Hofmann for real symmetric equations and their perturbations going back to a work of B. Dahlberg for Laplace's equation on Lipschitz domains, The first one is a certain bilinear estimate for a class of weak solutions and the second is a criterion which allows to identify the domain of the generator of the semi-group yielding such solutions.
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Taxonomy
TopicsMathematical Approximation and Integration · Mathematical functions and polynomials · Functional Equations Stability Results