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Estimates for elliptic systems from composite material

✍ Scribed by YanYan Li; Louis Nirenberg


Publisher
John Wiley and Sons
Year
2003
Tongue
English
Weight
332 KB
Volume
56
Category
Article
ISSN
0010-3640

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In this paper, we present a new bootstrap procedure for elliptic systems with two unknown functions. When combined with the L p -L q -estimates, it yields the optimal L ∞ -regularity conditions for the three well-known types of weak solutions: H 1 0 -solutions, L 1 -solutions and L 1 δ -solutions. T

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Recently [ 6 ] an existence as well as a uniqueness theorem for the discontinuous oblique derivative problem for nonlinear elliptic system of first order in the plane, see [12, 19, 231 wa.s proved, based on some a priori estimate from [ZO]. This estjmate, however, i Y deduced by reductio ad absurdum