This paper proves that, given the unit disk D on the the plane, 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 and its conormal derivative assigned on the boundary. The data on the boundary are regular functions, satisfying suitable mean properties.
Elliptic extensions in the disk with operators in divergence form / O.Arena; C.Giannotti. - In: BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY. - ISSN 0004-9727. - STAMPA. - 88-:(2013), pp. 51---55--. [10.1017/S000497271200069X]
Elliptic extensions in the disk with operators in divergence form
ARENA, ORAZIO;
2013
Abstract
This paper proves that, given the unit disk D on the the plane, 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
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