Non-local Gehring lemmas

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Auscher , Pascal; Bortz , Simon; Egert , Moritz; Saari , Olli;
  • Publisher: HAL CCSD
  • Subject: Fractional elliptic equations | Self-improvement properties | Gehring's lemma | [ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP] | Primary: 30L99; Secondary: 34A08, 42B25 | [ MATH.MATH-CA ] Mathematics [math]/Classical Analysis and ODEs [math.CA] | Reverse Hölder inequalities | Space of homogenous type | A∞ weights | Cp weights

46 pages. Submitted.; We prove a self-improving property for reverse Hölder inequalities with non-local right hand side. We attempt to cover all the most important situations that one encounters when studying elliptic and parabolic partial differential equations as well... View more
  • References (28)
    28 references, page 1 of 3

    2010 Mathematics Subject Classification. Primary: 30L99; Secondary: 34A08, 42B25.

    at its Boundaries”, ANR-12-BS01-0013. This material is based upon work supported by National

    Science Foundation under Grant No. DMS-1440140 while the authors were in residence at the MSRI

    in Berkeley, California, during the Spring 2017 semester. The second author was supported by the

    NSF INSPIRE Award DMS 1344235. The third author was supported by a public grant as part of the

    In Step 4, we pick λ0 := Cdℓ+2 supσ≥1 >σB w dμ (which is assumed finite otherwise

    observe that for x ∈ Br0 = B(x0, r0) and k ≥ 0,

    2 j(1−2α) . |x|−(n+1). [10] F.W. Gehring, The Lp-integrability of the partial derivatives of a quasiconformal mapping, Acta

    Math. 130 (1973), 265-277. 2 [11] M. Giaquinta, Multiple integrals in the calculus of variations and nonlinear elliptic systems,

    Annals of Mathematics Studies, 105. Princeton University Press, Princeton, NJ, 1983. 2 [12] M. Giaquinta and M. Struwe, On the partial regularity of weak solutions of nonlinear parabolic

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