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Applications of variational inequalities to the existence theorem on quadrature domains. (English) Zbl 0515.31001


MSC:

31A05 Harmonic, subharmonic, superharmonic functions in two dimensions
31B05 Harmonic, subharmonic, superharmonic functions in higher dimensions
49J40 Variational inequalities

Citations:

Zbl 0483.30001
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Full Text: DOI

References:

[1] Lipman Bers, An approximation theorem, J. Analyse Math. 14 (1965), 1 – 4. · Zbl 0134.05304
[2] C. M. Elliott and V. Janovsk√Ĺ, A variational inequality approach to Hele-Shaw flow with a moving boundary, Proc. Roy. Soc. Edinburgh Sect. A 88 (1981), no. 1-2, 93 – 107. · Zbl 0455.76043
[3] B. Gustafsson, Applications of variational inequalities to a moving boundary problem for Hele Shaw flows, TRITA-MAT-1981-9, Mathematics, Roy. Inst. Tech., Stockholm, p. 84. · Zbl 0605.76043
[4] Lars Inge Hedberg, Approximation in the mean by solutions of elliptic equations, Duke Math. J. 40 (1973), 9 – 16. · Zbl 0283.35035
[5] David Kinderlehrer and Guido Stampacchia, An introduction to variational inequalities and their applications, Pure and Applied Mathematics, vol. 88, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1980. · Zbl 0457.35001
[6] S. Richardson, Hele Shaw flows with a free boundary produced by the injection of fluid into a narrow channel, J. Fluid Mech. 56 (1972), 609-618. · Zbl 0256.76024
[7] Makoto Sakai, Quadrature domains, Lecture Notes in Mathematics, vol. 934, Springer-Verlag, Berlin-New York, 1982. · Zbl 0483.30001
[8] Makoto Sakai, Null quadrature domains, J. Analyse Math. 40 (1981), 144 – 154 (1982). · Zbl 0483.30002
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