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Hölder continuity of solutions of some degenerate elliptic differential equations

Published online by Cambridge University Press:  17 April 2009

Ahmed Mohammed
Affiliation:
Department of Mathematics & Computer Science, Faculty of Science, Kuwait University, P.O.Box 5969, Safat 13060, Kuwait e-mail: [email protected]
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Abstract

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Weak solutions of the degenerate elliptic differential equation Lu := −div(A (x)∇u)+b·∇u+Vu = f, with |b|2ω−1, V, f in some appropriate function spaces, will be shown to be Hölder continuous.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2000

References

[1]Chanillo, S. and Wheedem, R., ‘Existence and estimates of Green's function for degenerate elliptic equations’, Ann. Scoula Norm. Sup. Pisa Cl. Sci. 15 (1988), 309340.Google Scholar
[2]Chiarenza, F., Fabes, E. and Garofalo, N., ‘Harnack's inequality for Schrödinger operators and continuity of solutions’, Proc. Amer. Math. Soc. 98 (1986), 415425.Google Scholar
[3]Fabes, E., Jerison, D. and Kenig, C., ‘The Wiener test for degenerate elliptic equations’, Ann. Inst. Fourier (Grenoble) 32 (1982), 151182.CrossRefGoogle Scholar
[4]Gilbarg, D. and Trudinger, N.S., Elliptic partial differential equations of second order, (2nd edition) (Springer-Verlag, Berlin, Heidelberg, New York, 1983).Google Scholar
[5]Gutierrez, C.E., ‘Harnack's inequality for degenerate Schrödinger operators’, Trans. Amer. Math. Soc. 312 (1989), 403419.Google Scholar
[6]Heinonen, J., Kilpeläinen, T. and Martio, O., Nonlinear potential theory of degenerate elliptic equations (Oxford University Press Inc., Oxford, 1993).Google Scholar
[7]Kurata, K., ‘Continuity and Harnack's inequality for solutions of elliptic partial differential equations of second order’, Indiana Univ. Math. 54 (1995), 511550.Google Scholar