Construction of a singular elliptic-harmonic measure
- 133 Downloads
The authors study an example, suggested by E. De Giorgi, of a second-order uniformly elliptic partial differential operator in divergence form with continuous coefficients on a smooth domain in the plane such that the associated “harmonic measure“ on the boundary is not absolutely continuous with respect to the ordinary surface measure.
KeywordsDifferential Operator Number Theory Divergence Form Algebraic Geometry Topological Group
Unable to display preview. Download preview PDF.
- CAFFARELLI, L., FABES, E., KENIG, C.: Completely singular elliptic-harmonic measures. To appear on Indiana University Mathematics JournalGoogle Scholar
- CAFFARELLI, L., FABES, E., MORTOLA, S., SALSA, S.: Boundary behavior of nonnegative solutions of elliptic operators in divergence form. To appear on Indiana University Mathematics JournalGoogle Scholar
- DAHLBERG, B.E.J.: Estimates of harmonic measures. Arch. Rat. Mech. Analysis65, 275–288 (1977)Google Scholar
- LITTMAN, W., STAMPACCHIA, G., WEINBERGER, H.F.: Regular points for elliptic equations with discontinuous coefficients. Ann. Sc. Norm. Sup. Pisa, Cl. Sci., Ser. III,XVII, 45–79 (1963)Google Scholar
- MEYERS, N.G.: An LP-estimate for the gradient of solutions of second order elliptic divergence equations. Ann. Sc. Norm. Sup. Pisa, Cl. Sci., Ser. III,XVII, 189–206 (1963)Google Scholar
- MOSER, J.: On Harnack's theorem for elliptic differential equations. Comm. Pure Appl. Math.XIV, 577–591 (1961)Google Scholar
- PROTTER, M., WEINBERGER, H.F.: Maximum principles in differential equations. Englewood Cliffs N.J., Prentice-Hall Inc. 1967Google Scholar
- ZYGMUND, A.: Trigonometric series. London-New York. Cambridge University Press 1959Google Scholar