A pointwise differential inequality and second-order regularity for nonlinear elliptic systems
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AbstractA sharp pointwise differential inequality for vectorial second-order partial differential operators, with Uhlenbeck structure, is offered. As a consequence, optimal second-order regularity properties of solutions to nonlinear elliptic systems in domains in $${\mathbb R^n}$$ R n are derived. Both local and global estimates are established. Minimal assumptions on the boundary of the domain are required for the latter. In the special case of the p-Laplace system, our conclusions broaden the range of the admissible values of the exponent p previously known.
1985 ◽
Vol 112
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pp. 178-189
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1982 ◽
Vol 99
(1)
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pp. 1-17
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1980 ◽
Vol 94
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pp. 155-172
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1990 ◽
Vol 9
(6)
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pp. 535-544
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1990 ◽
Vol 15
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pp. 241-258
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1983 ◽
Vol 8
(6)
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pp. 643-665
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