2010
DOI: 10.1007/s00229-010-0367-z
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A priori estimates for the difference of solutions to quasi-linear elliptic equations

Abstract: A priori estimates for finite-difference approximations for the first and second-order derivatives are obtained for solutions of parabolic equations described in the title.

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Cited by 21 publications
(7 citation statements)
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“…Proposition 2.4. (see [6]) Let a, b ∈ R N and r ∈ (1, ∞). Then there exists a constant c r > 0 such that 13) and also in this case there is a constant c r ∈…”
Section: Preliminaries and Intermediate Resultsmentioning
confidence: 99%
“…Proposition 2.4. (see [6]) Let a, b ∈ R N and r ∈ (1, ∞). Then there exists a constant c r > 0 such that 13) and also in this case there is a constant c r ∈…”
Section: Preliminaries and Intermediate Resultsmentioning
confidence: 99%
“…where s, r ∈ R n and p > 1. But as noted in [13, p. 74] (see also [1,Section 4]), this expression is nonnegative. Thus, T is monotone.…”
Section: P(•)-poincaré Implies P(•)-neumannmentioning
confidence: 93%
“…Now consider the domain E − . By [13, p. 43] (see also [1,Section 4]) we have that for r, s ∈ R n and 1 < p ≤ 2,…”
Section: P(•)-poincaré Implies P(•)-neumannmentioning
confidence: 99%
“…By virtue of Theorem 3.2, it suffices to show that u p(·), ≤ C u Wμ ( ,∂ ) for all u ∈ W 1,p(·) ( ), and for some constant C > 0. To show this assertion, one just follow the same argument as in [3,Theorem 4.24], with the help of Theorem 3.11.…”
Section: The Variable Exponent Maz'ya Spacementioning
confidence: 93%
“…REMARK 6.5. By following the arguments given in the beautiful result by Biegert [3,Theorem 5.10], it may be possible to show that if we assume the conditions of Corollary 6.4, the (unique) weak solution of (6.27) is bounded on . Since this is not the main purpose of this article, we do not go into further details here.…”
Section: Some Examples Of Non-smooth Domainsmentioning
confidence: 98%