A first-order approach to boundary value problems for elliptic equations with rough complex coefficients and fractional regularity data




Date(s) : 01/02/2016   iCal
10 h 00 min - 11 h 00 min

We consider the well-posedness of boundary value problems associated with elliptic equations $\div A \nabla u = 0$ with complex $t$-independent coefficients on the upper half-space, and with boundary data in Besov–Hardy–Sobolev (BHS) spaces. A key tool in our study is a theory of BHS spaces adapted to first-order operators which are bisectorial with bounded $H^\infty$ functional calculus, and which satisfy certain off-diagonal estimates.
Within a range of exponents determined by properties of adapted BHS spaces, we show that well-posedness of a boundary value problem is equivalent to an associated projection being an isomorphism. As an application, for equations with real coefficients, we extend known well-posedness results for the Regularity problem with data in Hardy and Lebesgue spaces to a large range of BHS spaces.
This work is part of a doctoral thesis supervised by Pascal Auscher (Paris-Sud) and Pierre Portal (Australian National University).

Alex AMENTA,  Australian National University

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