Gradient estimates in non-linear potential theory

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

Volumn 20, Issue 2, 2009, Pages 179-190

  Duzaar, Frank ^a   Mingione, Giuseppe ^b,c  

^a UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

^b UNIVERSITY OF PARMA   (Italy)

^c NONE

Author keywords

P Laplacian; Regularity; Wolff potential

Indexed keywords

EID: 84876085339     PISSN: 11206330     EISSN: 17200768     Source Type: Journal    
DOI: None     Document Type: Article

References (25)

1. Acerbi E. - Mingione G.: Gradient estimates for a class of parabolic systems. Duke Math. J. 136 (2007), 285-320.
2. Adams D. R. - Bagby R. J.: Translation-dilation invariant estimates for Riesz potentials. Indiana Univ. Math. J. 23 (1974), 1051-1067.
3. Adams D. R. - Hedberg L. I.: Function spaces and potential theory. Grundlehren der Mathematischen Wissenschaften 314. Springer-Verlag, Berlin, 1996.
4. Adams D. R. - Meyers N. G.: Thinnes and Wiener criteria for non-linear potentials. Indiana Univ. Math. J. 22 (1972), 169-197.
5. Adams R.A.: Sobolev Spaces. Academic Press, New York, 1975.
6. Boccardo L.: Problemi differenziali ellittici e parabolici con dati misure [Elliptic and parabolic differential problems with measure data]. Boll. Un. Mat. Ital. A (7) 11 (1997), 439-461.
7. Boccardo L. - Gallouët T.: Nonlinear elliptic and parabolic equations involving measure data. J. Funct. Anal. 87 (1989), 149-169.
8. Boccardo L. - Gallouët T.: Nonlinear elliptic equations with right-hand side measures. Comm. Partial Differential Equations 17 (1992), 641-655.
9. DiBenedetto E.: Degenerate parabolic equations. Universitext. Springer-Verlag, New York, 1993.
10. DiBenedetto E. - Manfredi J. J.: On the higher integrability of the gradient of weak solutions of certain degenerate elliptic systems. Amer. J. Math. 115 (1993), 1107-1134.
11. De Giorgi E.: Sulla differenziabilità e l'analiticità delle estremali degli integrali multi-pli regolari. Mem. Accad. Sci. Torino Cl. Sci. Fis. Mat. Nat. (III) 125 3 (1957), 25-43.
12. Duzaar F. - Mingione G.: Gradient estimates via non-linear potentials. Preprint 2009.
13. Grüter M. - Widman K. O.: The Green function for uniformly elliptic equations. manuscripta math. 37 (1982), 303-342.
14. Havin M. - Maz'ja V. G.: A nonlinear potential theory. Russ. Math. Surveys 27 (1972), 71-148.
15. Hedberg L. I. - Wolff T.: Thin sets in nonlinear potential theory. Ann. Inst. Fourier (Grenoble) 33 (1983), 161-187.
16. p-estimates for degenerated elliptic operators. Studia Math. 75 (1983), 293-312.
17. Kilpeläinen T. - Malý J.: The Wiener test and potential estimates for quasilinear elliptic equations. Acta Math. 172 (1994), 137-161.
18. Kristensen J. - Mingione G.: The singular set of minima of integral functionals. Arch. Ration. Mech. Anal. 180 (2006), 331-398. (Pubitemid 43536188)
19. Mingione G.: The Calderón-Zygmund theory for elliptic problems with measure data. Ann Scu. Norm. Sup. Pisa Cl. Sci. (5) 6 (2007), 195-261.
20. Mingione G.: Gradient estimates below the duality exponent. Preprint (2008).
21. Mingione G.: Towards a non-linear Calderón-Zygmund theory. Quaderni di Matema-tica (Alvino, Mercaldo, Murat & Peral eds.) (2009).
22. Mingione G.: Gradient potential estimates. Preprint (2008).
23. Talenti G.: Elliptic equations and rearrangements. Ann Scu. Norm. Sup. Pisa Cl. Sci. (4) 3 (1976), 697-717.
24. Trudinger N. S. - Wang X. J.: On the weak continuity of elliptic operators and applications to potential theory. Amer. J. Math. 124 (2002), 369-410.
25. Trudinger N. S. - Wang X. J.: Quasilinear elliptic equations with signed measure data. Disc. Cont. Dyn. Systems A 23 (2009), 477-494.