Let phi_0 and phi_1 be regular functions on the boundary bD of the unit disk D in R^2, such that the integrals over bD of phi_1(t) e of sin(t)* (phi_1(t) - phi_0(t)) are both vanishing. It is proved that there exist a linear second order uniformly elliptic operator L in divergence form with bounded measurable coefficients and a function u in W^{1,p}(D), 1 < p <2, such that Lu=0 in D and with u|_{bD}= phi_0 and the conormal derivative \partial u/\partial N|_{bD}=phi_1.

Elliptic extensions in the disk with operators in divergence form

GIANNOTTI, Cristina
2013-01-01

Abstract

Let phi_0 and phi_1 be regular functions on the boundary bD of the unit disk D in R^2, such that the integrals over bD of phi_1(t) e of sin(t)* (phi_1(t) - phi_0(t)) are both vanishing. It is proved that there exist a linear second order uniformly elliptic operator L in divergence form with bounded measurable coefficients and a function u in W^{1,p}(D), 1 < p <2, such that Lu=0 in D and with u|_{bD}= phi_0 and the conormal derivative \partial u/\partial N|_{bD}=phi_1.
2013
262
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11581/250759
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