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Transactions of the American Mathematical Society

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Estimates of the Caccioppoli-Schauder type in weighted function spaces

Author: Giovanni Maria Troianiello
Journal: Trans. Amer. Math. Soc. 334 (1992), 551-573
MSC: Primary 35B45; Secondary 35J25, 46E35
MathSciNet review: 1049865
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Abstract: We deal with imbeddings of certain weighted function spaces as well as with the corresponding norm estimates for solutions to second order elliptic problems. We redemonstrate some results of Gilbarg and Hörmander by a technique, entirely different from theirs, which enables us to cover a range of parameters excluded by them.

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  • [1] P. Bolley, J. Camus, and G. Métivier, Estimations de Schauder et régularité hölderienne pour une classe de problèmes aux limites singuliers, Comm. Partial Differential Equations 11 (1986), 1135-1203. MR 855524 (88a:35036)
  • [2] S. Campanato, Proprietà di Hölderianità di alcune classi di funzioni, Ann. Scuola Norm. Sup. Pisa Sci. Fis. Mat. 17 (1963), 175-188. MR 0156188 (27:6119)
  • [3] -, Equazioni ellittiche del secondo ordine e spazi $ {L^{2,\lambda }}$, Ann. Mat. Pura Appl. 69 (1965), 321-382.
  • [4] -, Su un teorema di interpolazione di G. Stampacchia, Ann. Scuola Norm Sup. Pisa Sci. Fis. Mat. 20 (1966), 649-652. MR 0209864 (35:760)
  • [5] S. Campanato and G. Stampacchia, Sulle maggiorazioni $ {L^p}$ nella teoria delle equazioni ellittiche, Boll. Un. Mat. Ital. 20 (1965), 393-399. MR 0192169 (33:396)
  • [6] C. Fefferman and E. Stein, $ {H^p}$ spaces of several variables, Acta Math. 129 (1972), 137-193. MR 0447953 (56:6263)
  • [7] D. Gilbarg and L. Hörmander, Intermediate Schauder estimates, Arch. Rational Mech. Anal. 74 (1980), 297-318. MR 588031 (82a:35038)
  • [8] F. John and L. Nirenberg, On functions of bounded mean oscillation, Comm. Pure Appl. Math. 14 (1961), 415-426. MR 0131498 (24:A1348)
  • [9] G. M. Lieberman, Intermediate Schauder estimates for oblique derivative problems, Arch. Rational Mech. Anal. 93 (1986), 129-134. MR 823115 (87j:35112)
  • [10] J. Nečas, Les méthodes directs en théorie des équations elliptiques, Masson, Paris, 1967.
  • [11] D. W. Stroock and S. R. J. Varadhan, Multidimensional diffusion processes, Springer, Berlin, Heidelberg, and New York, 1979. MR 532498 (81f:60108)
  • [12] G. M. Troianiello, Elliptic differential equations and obstacle problems, Plenum, New York, 1987. MR 1094820 (92b:35004)
  • [13] -, A class of weighted function spaces and intermediate Caccioppoli-Schauder estimates, Journées Équations aux Dérivées Partielles, St.-Jean-de-Monts, 1988.

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