Higher integrability results

Franciosi, Michelangelo; Moscariello, Gioconda

doi:10.1007/bf01171490

Cited by 29 publications

(19 citation statements)

References 12 publications

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“…From theorem 2, using the same arguments as those of [3,5] and the well known Gehring theorem [4,9,11] it is easy to deduce the estimate…”

Section: The Resultsmentioning

confidence: 93%

Maximum Principles for Second Order Elliptic Equations in Nondivergence Form and Applications

Almahameed¹

2008

J. of Mathematics and Statistics

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Abstract:The main objectives of this study were to introduce a maximum principle for second order elliptic equations in nondivergence form and to use a nondivergence technique called the ABP method to establish the maximum principles in small domains. The advantage of this work was that we obtain a maximum principle for equations with discontinuous coefficients of the leading terms and the ABP estimate was a bound for solutions of uniformly elliptic equations written in nondivergence form with measurable coefficients. It was an essential tool in the regularity theory for fully nonlinear equations.

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“…From theorem 2, using the same arguments as those of [3,5] and the well known Gehring theorem [4,9,11] it is easy to deduce the estimate…”

Section: The Resultsmentioning

confidence: 93%

Maximum Principles for Second Order Elliptic Equations in Nondivergence Form and Applications

Almahameed¹

2008

J. of Mathematics and Statistics

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“…The estimates of arrangements of the function f ∈ RH α,β (B) are obtained in various works (see [3,10,11,13,14]). These estimates intended to prove that the rearrangement f * (or f * ) belongs to the Conclusion The sharp estimates of the self-improvement of the summability exponents presented in Corollary 4.2 have been known earlier (see, e.g., [1,12], [8, p. 173]).…”

Section: Remark 41mentioning

confidence: 99%

The reverse Hölder inequality for power means

Didenko

Korenovskyi

2012

J Math Sci

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For a function ϕ non-negative on the interval [0, 1], the power mean of order α = 0 is defined by the equality Mαϕ(t) = 1 t t 0 ϕ α (u) du 1/α , 0 < t ≤ 1. We consider the class RH α,β (B) of functions ϕ satisfying the reverse Hölder inequality M β ϕ ≤ B · Mαϕ at some α < β, α · β = 0, B > 1. The sharp estimates for the summability exponents of the compositions of power means are established. As a result, we determine the properties of self-improvement of the summability exponents of functions from RH α,β (B).Keywords. Power means, property of self-improvement of the summability exponents, reverse Hölder inequality.

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“…Estimates of equimeasurable rearrangements are often useful for the investigation of properties of functions from these classes. Thus, in [4], an estimate for a nonincreasing rearrangement was used for giving a simpler proof (as compared with those known earlier) of the main property of functions of the Gehring class (an increase in the summation index). In [5,6], an analogous property for functions satisfying the Muckenhoupt condition was also established with the use of an estimate for an equimeasurable rearrangement.…”

Section: The Function F μ [ ]mentioning

confidence: 99%