The Harnack inequality and the Hölder property of solutions of nonlinear elliptic equations with a nonstandard growth condition

Differential Equations

Volumn 33, Issue 12, 1997, Pages 1653-1663

  Alkhutov, Yu A ^a  

^a VLADIMIR STATE UNIVERSITY   (Russian Federation)

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[No Author keywords available]

Indexed keywords

EID: 22044455109     PISSN: 00122661     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (16)

1. E. De Giorgi, Mem. Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur., 3, No. 3, 25-43 (1957).
2. J. Nash, Amer. J. Math., 80, 931-954 (1958).
3. J. Moser, Comm. Pure Appl. Math., 14, 577-591 (1961).
4. O. A. Ladyzhenskaya and N. N. Ural'tseva, Tr. Mat. In-ta Akad. Nauk SSSR, 73, 172-220 (1964).
5. J. Serrin, Acta Math., 111, 247-337 (1964).
6. V. V. Zhikov, Izv. Akad. Nauk SSSR. Ser. Mat., 50, No. 4, 675-711 (1986).
7. V. V. Zhikov, Mat. Sb., 183, No. 8, 47-84 (1992).
8. V. V. Zhikov, Dokl. RAN, 345, No. 1, 10-14 (1995).
9. V. Zhikov, Russian Journal of Math. Physics, 3, No. 2, 249-269 (1995).
10. V. Zhikov, Russian Journal of Math. Physics, 5, No. 1, 105-116 (1997).
11. Fan Xianling, A Class of De Giorgi Type and Hölder Continuity of Minimizers of Variational with m(x)-Growth Condition, Lanzhou University, China (1995).
12. E. Acerbi and N. Fusco, Calc. Var., 1-16 (1994).
13. N. S. Trudinger, Comm. Pure Appl. Math., 20, 721-747 (1967).
14. D. Gilbarg and N. Trudinger, Second-Order Elliptic Partial Differential Equations [Russian translation], Moscow (1989).
15. E. B. Fabes and D. W. Stroock, Duke Math. J., 51, No. 4, 997-1016 (1984).
16. G. John and L. Nirenberg, Comm. Pure Appl. Math., 14, 415-426 (1961).