A fractional Gehring lemma, with applications to nonlocal equations

Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni

Volumn 25, Issue 4, 2014, Pages 345-358

  Kuusi, Tuomo ^a   Mingione, Giuseppe ^b   Sire, Yannick ^c  

^a AALTO UNIVERSITY   (Finland)

^b UNIVERSITY OF PARMA   (Italy)

^c AIX MARSEILLE UNIVERSITY   (France)

Author keywords

Elliptic equations; Non local operators; Self improving properties

Indexed keywords

MATHEMATICAL TECHNIQUES;

ELLIPTIC EQUATIONS; NON-LOCAL EQUATIONS; NONLOCAL; REGULARITY PROPERTIES; SELF-IMPROVING PROPERTIES;

INTEGRODIFFERENTIAL EQUATIONS;

EID: 84911414518     PISSN: 11206330     EISSN: 17200768     Source Type: Journal    
DOI: 10.4171/RLM/683     Document Type: Article

References (16)

1. R. F. Bass - H. Ren: Meyers inequality and strong stability for stable-like operators, J. Funct. Anal. 265 (2013), 28-48.
2. B. Bojarski - T. Iwaniec: Analytical foundations of the theory of quasiconformal mappings in Rn, Ann. Acad. Sci. Fenn. Ser. A I Math. 8 (1983), 257-324.
3. L. Caffarelli - C. H. Chan - A. Vasseur: Regularity theory for parabolic nonlinear integral operators, J. Amer. Math. Soc. 24 (2011), 849-869.
4. J. R. Dorronsoro: A characterization of potential spaces, Proc. Amer. Math. Soc. 95 (1985), 21-31.
5. A. Elcrat - N. Meyers: Some results on regularity for solutions of non-linear elliptic systems and quasi-regular functions, Duke Math. J. 42 (1975), 121-136.
6. N. Fusco - C. Sbordone: Higher integrability of the gradient of minimizers of functionals with nonstandard growth conditions, Comm. Pure Appl. Math. 43 (1990), 673-683.
7. F. W. Gehring: The Lp-integrability of the partial derivatives of a quasiconformal mapping, Acta Math. 130 (1973), 265-277.
8. M. Giaquinta - G. Modica: Regularity results for some classes of higher order nonlinear elliptic systems, J. reine angew. Math. (Crelles J.) 311/312 (1979), 145-169.
9. T. Iwaniec: The Gehring lemma, Quasiconformal mappings and analysis (Ann Arbor, MI, 1995), 181-204, Springer, New York, 1998.
10. M. Kassmann: A priori estimates for integro-differential operators with measurable kernels, Calc. Var. PDE 34 (2009), 1-21.
11. J. Kinnunen - J. L. Lewis: Higher integrability for parabolic systems of p-Laplacian type, Duke Math. J. 102 (2000), 253-271.
12. T. Kuusi - G. Mingione: Universal potential estimates, J. Funct. Anal. 262 (10), 4205-4269.
13. T. Kuusi - G. Mingione - Y. Sire: Nonlocal self-improving properties, 2015, 8(1):57-114.
14. N. G. Meyers: An Lp-estimate for the gradient of solutions of second order elliptic divergence equations, Ann. Scuola Norm. Sup. Pisa C. Sci. (3) 17 (1963), 189-206.
15. G. Mingione: The singular set of solutions to non-differentiable elliptic systems, Arch. Ration. Mech. Anal. 166 (2003), 287-301.
16. E. M. Stein: The characterization of functions arising as potentials, Bull. Amer. Math. Soc. 67 (1961), 102-104.