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- W1969578579 abstract "Abstract We prove regularity results for certain degenerate quasilinear elliptic systems with coefficients which depend on two different weights. By using Sobolev- and Poincare inequalities due to Chanillo and Wheeden [S. Chanillo, R.L. Wheeden, Weighted Poincare and Sobolev inequalities and estimates for weighted Peano maximal functions, Amer. J. Math. 107 (1985) 1191–1226; S. Chanillo, R.L. Wheeden, Harnack's inequality and mean-value inequalities for solutions of degenerate elliptic equations, Comm. Partial Differential Equations 11 (1986) 1111–1134] we derive a new weak Harnack inequality and adapt an idea due to L. Caffarelli [L.A. Caffarelli, Regularity theorems for weak solutions of some nonlinear systems, Comm. Pure Appl. Math. 35 (1982) 833–838] to prove a priori estimates for bounded weak solutions. For example we show that every bounded weak solution of the system − D α ( a α β ( x , u , ∇ u ) D β u i ) = 0 with | x | 2 | ξ | 2 ⩽ a α β ξ α ξ β ⩽ | x | τ | ξ | 2 , | x | 1 , τ ∈ ( 1 , 2 ) is Holder continuous. Furthermore we derive a Liouville theorem for entire solutions of the above systems." @default.
- W1969578579 created "2016-06-24" @default.
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- W1969578579 date "2008-04-01" @default.
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- W1969578579 title "Regularity results for degenerate elliptic systems" @default.
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- W1969578579 doi "https://doi.org/10.1016/j.anihpc.2007.02.008" @default.
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