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A nonvariational second order elliptic operator with singular elliptic measure

Authors: Luciano Modica, Stefano Mortola and Sandro Salsa
Journal: Proc. Amer. Math. Soc. 84 (1982), 225-230
MSC: Primary 35J25
MathSciNet review: 637173
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Abstract: We exhibit an example which proves that the elliptic measure for a second-order operator of the form $ \Sigma _{i,j = 1}^n{a_{ij}}D_{ij}^2$ with continuous coefficients can be singular with respect to the surface measure on the boundary of a smooth two-dimensional domain.

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  • [1] A. D. Alexandrov, Majorization of solutions of second-order linear equations, Amer. Math. Soc. Transl. (2) 68 (1968), 120-143.
  • [2] L. Caffarelli, E. Fabes and C. Kenig, Completely singular elliptic harmonic measures, Indiana Univ. Math. J. (to appear). MR 632860 (83a:35033)
  • [3] N. G. Meyers, An $ {L^p}$-estimate for the gradient of solutions of second order elliptic divergence equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci. Ser. III 17 (1963), 189-206. MR 0159110 (28:2328)
  • [4] L. Modica and S. Mortola, Construction of a singular elliptic-harmonic measure, Manuscripta Math. 33 (1980), 81-98. MR 596380 (81m:31001)
  • [5] M. Protter and H. F. Weinberger, Maximum principles in differential equations, Prentice-Hall, Englewood Cliffs, N.J., 1967. MR 0219861 (36:2935)
  • [6] C. Pucci, Limitazioni per soluzioni di equazioni ellittiche, Ann. Mat. Pura Appl. (4) 74 (1966), 15-30. MR 0214905 (35:5752)
  • [7] G Talenti, Equazioni lineari ellittiche in due variabili, Le Matematiche 21 (1966), 339-376. MR 0204845 (34:4681)
  • [8] A. Zygmund, Trigonometric series, Cambridge Univ. Press, London and New York, 1959. MR 0107776 (21:6498)

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