On Morrey's estimate of the Sobolev norms of solutions of elliptic equations

Mathematical Notes

Volumn 79, Issue 3-4, 2006, Pages 413-430

  Shaposhnikov, S V ^a  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

Elliptic equation; Fubini's theorem; H lder's inequality; Lebesgue integral; Sobolev norm; Sobolev space; Weak solution

Indexed keywords

EID: 33646009699     PISSN: 00014346     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11006-006-0046-2     Document Type: Article

References (7)

1. C. B. Morrey, Multiple Integrals in the Calculus of Variations, Springer-Verlag, Berlin-Heidelberg-New York, 1966.
2. V. I. Bogachev and M. Röckner, "A generalization of Hasminskii's theorem on existence of invariant measures for locally integrable drifts," Tear. Veroyatnost. i Primenen. [Theory Probab. Appl.], 45 (2000), no. 3, 417-436.
3. V. I. Bogachev, N. V. Krylov, and M. Röckner, "On regularity of transition probabilities and invariant measures of singular diffusions under minimal conditions," Comm. Partial Diff. Eq., 26 (2001), no. 11-12, 2037-2080.
4. D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin-New York, 1977; Russian translation: Nauka, Moscow, 1989.
5. O. A. Ladyzhenskaya and N. N. Ural'tseva, Linear and Quasilinear Elliptic Equations [in Russian], Nauka, Moscow, 1973.
6. G. Stampacchia, Équations elliptiques du second ordre à coefficients discontinus, Les Presses de l'Université de Montréal, 1966.
7. N. S. Trudinger, "Linear elliptic operators with measurable coefficients," Ann. Scu. Norm. Sup. Pisa (3), 27 (1973), 265-308.