Estimates on the generalized Morrey spaces L2,λφ and BMOψ for linear elliptic systems

Indiana University Mathematics Journal

Volumn 45, Issue 2, 1996, Pages 397-439

  Huang, Qingbo ^a  

^a Temple University   (United States)

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EID: 0005496743     PISSN: 00222518     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (25)

1. P. ACQUISTAPACE, On BMO Regularity for linear elliptic systems, Ann. Mat. Pura Appl. 161 (1992), 231-269.
2. S. AGMON, A. DOUGLIS & L. NIRENBERG, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II, Comm. Pure Appl. Math. 17 (1964), 35-72.
3. A. AIZENMAN & B. SIMON, Brownian motion and Harnack's inequality for Schrödinger operators, Comm. Pure Appl. Math. 35 (1982), 209-273.
4. C. C. BURCH, The Dini condition and regularity of weak solutions of elliptic equations, J. Diff. Eq. 30 (1978), 308-323.
5. L. CAFFARELLI, Elliptic second order equations, Rend. Sem. Mat. Fis. Milan 58 (1988), 253-284.
6. 2,λ, Ann. Mat. Pura. Appl. 69 (1965), 321-382.
7. Y.Z. CHEN & L.C. Wu, Elliptic equations and elliptic systems of second order, Academic Press, Beijing, China, 1991.
8. p-regularity for systems of PDE's with coefficients in VMO, Nonlinear Analysis, Function Spaces and Applications, Proceedings of the Spring School (Prague, May 1994), vol. 5, Prometheus Publishing House, pp. 1-32.
9. F. CHIARENZA, E. F. FABES & N. GAROFALO, Harnack's inequality for Schrödinger operators and the continuity of solutions, Proc. Amer. Math. Soc. 98 (1986), 415-425.
10. 2,p -soluability of the Dirichlet problem for nondivergence elliptic equations with VMO coefficients, Trans. Amer. Math. Soc. 336 (1993), 841-853.
11. M. CRANSTON, E. B. FABES & Z. ZHAO, Conditional gauge and potential theory for the Schrü-dinger operator, Trans. Amer. Math. Soc. 307 (1988), 171-194.
12. DI FAZIO & M. A. RAGUSA, Interior Estimates in Morrey spaces for strong solutions to non divergence form equations with discontinuous coefficients, J. Funct. Anal. 112 (1993), 241-256.
13. M. GIAQUIKTA, Multiple integrals in the calculus of variations and nonlinear elliptic systems, vol. #105 Ann. of Math Studies, Princeton Univ. Press, Princeton, NJ, 1983.
14. D. GILBARG & N. TRUDINGER, Elliptic partial differential equations of second order, 2nd edition, Springer-Verlag, 1983.
15. C. E. GUTIERREZ, Harnack's inequality for degenerate Schrodinger operators, Trans. Amer. Math. Soc. 312 (1989), 403-419.
16. A. M. HINZ & H. KALF, Subsolution estimates and Harnack's inequality for Schrodinger operators, J. Reine Angew. Math. 404 (1990), 118-134.
17. S. JANSON, On functions with conditions on the mean oscillation, Ark. Mat. 14 (1976), 189-196.
18. K. KURATA, Continuity and Harnack's inequality for solutions of elliptic partial differential equations of second order, Indi. Univ. Math. J. 43 (1994), 411-440.
19. O. A. LADYZHENSKAJA & N. N. URAL'TSEVA, Linear and quasilinear elliptic equations, Academic Press, New York and London, 1968.
20. D. SARASON, Functions of vanishing mean oscillation, Trans. Amer. Math. Soc. 207 (1975), 391-405.
21. B. SIMON, Schrödinger semigroups, Bull. Amer Math. Soc. 7 (1982), 447-526.
22. S. SPANNE, Some function spaces defined using the mean oscillation over cubes, Ann. Scuola Norm. Sup. Pisa 19 (1965), 593-60S.
23. G. STAMPACCHIA, Le probleme de Dirichlet pour les equations elliptiques du second ordre a coefficients discontinus, Ann. Inst. Fourier(Grenoble) 15 (1965), 189-257.
24. E. M. STEIN, Harmonic Analysis: Real-Variable Methods, Orthogonality and Oscillatory Integrals, Princeton Univ. Press, 1993.
25. -1,α and analytic semigroups, Diff. Int. Eq. 1 (1988), 473-493.