no. 3
An exponential transform and regularity of free boundaries in two dimensions
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 26 (1998) no. 3, pp. 507-543. 
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     author = {Gustafsson, Bj\"orn and Putinar, Mihai},
     title = {An exponential transform and regularity of free boundaries in two dimensions},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {507--543},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 26},
     number = {3},
     year = {1998},
     mrnumber = {1635702},
     zbl = {0937.32007},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1998_4_26_3_507_0/}
}
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Gustafsson, Björn; Putinar, Mihai. An exponential transform and regularity of free boundaries in two dimensions. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 26 (1998) no. 3, pp. 507-543. http://www.numdam.org/item/ASNSP_1998_4_26_3_507_0/

[Af] L.V. Ahlfors, Finitely generated Kleinian groups, Amer. J. Math. 86 (1964), 413-429. | MR | Zbl

[Ah-Sh] D. Aharonov - H.S. Shapiro, Domains in which analytic functions satisfy quadrature identities, J. Analyse Math. 30 (1976), 39-73. | MR | Zbl

[Be] L. Bers, An approximation theorem, J. Anal. Math. 14 (1965), 1-4. | MR | Zbl

[Br] L. Brown, The determinant invariant for operators with trace class self-commutator, In: "Proc. Conference on Operator Theory", Lecture Notes in Math. Vol. 345, Springer, Berlin, 1973. | MR | Zbl

[Ca] L. Caffarelli, Compactness methods infree boundary problems, Comm. Partial Differential Equations 5 (1980), 427-448. | MR | Zbl

[Cd-Z] A.P. Calderon - A. Zygmund, Local properties of solutions of elliptic partial differential equations, Studia Math. 20 (1961), 171-225. | MR | Zbl

[C-Pi] R.W. Carey - J.D. Pincus, An exponential formula for determining functions, Indiana Univ. Math. J. 23 (1974), 1031-1042. | MR | Zbl

[Cl1] K. Clancey, A kernel for operators with one-dimensional self-commutator, Integral Equations Operator Theory 7 (1984), 441-458. | MR | Zbl

[Cl2] K. Clancey, Hilbert space operators with one-dimensional self-commutator, J. Operator Theory 13 (1985), 265-289. | MR | Zbl

[E-G] L.C. Evans - R.F. Gariepy, Measure Theory and Fine Properties of Functions, CRC Press, Boca Raton, 1992. | MR | Zbl

[D] P.J. Davis, The Schwarz Function and its Applications, Carus Mathematical Monographs, Math. Assoc. Amer., 1974. | MR | Zbl

[Gu1] B. Gustafsson, Quadrature identities and the Schottky double, Acta Appl. Math. 1 (1983), 209-240. | MR | Zbl

[Gu2] B. Gustafsson, Singular and special points on quadrature domains from an algebraic geometric point of view, J. Anal. Math. 51 (1988), 91-117. | MR | Zbl

[He-Ho] J.W. Helton - R. Howe, Traces of commutators of integral operators, Acta Math. 135 (1975), 271-305. | MR | Zbl

[Hm] L. Hörmander, An Introduction to Complex Analysis in Several Variables, North-Holland, Amsterdam, 1989. | MR | Zbl

[K-Mg] L. Karp - A. Margulis, On the Newtonian potential theory for unbounded sources and its applications to free boundary problems, J. Anal. Math. 70 (1996), 1-63. | MR | Zbl

[K-N] M.G. Krein - A.A. Nudelman, The Markov moment problem and extremal problems, Transl. Math. Monographs, vol. 50, Amer. Math. Soc., Providence, R.I., 1977. | MR | Zbl

[MP] M. Martin - M. Putinar, Lectures on Hyponormal Operators, Birkhäuser, Basel, 1989. | MR | Zbl

[Pi] J.D. Pincus, Commutators and systems of singular integral equations I, Acta Math. 121 (1968), 219-249. | MR | Zbl

[Pi-Rv] J.D. Pincus - J. Rovnyak, A representation for determining functions, Proc. Amer. Math. Soc. 22 (1969), 498-502. | MR | Zbl

[P1] M. Putinar, Extremal solutions of the two-dimensional L-problem of moments, J. Funct. Anal. 136 (1996), 331-364. | MR | Zbl

[P2] M. Putinar, Linear analysis of quadrature domains, Ark. Mat. 33 (1995), 357-376. | MR | Zbl

[P3] M. Putinar, Extremal solutions of the two-dimensional L-problem of moments II, J. Approx. Theory (to appear). | MR | Zbl

[Re] Yu G. Reshetnyak, Generalized derivatives and differentiability almost everywhere, Mat. Sb. 75 (1968), 323-334 (translated from Russian). | MR | Zbl

[Ro] J.F. Rodrigues, Obstacle Problems in Mathematical Physics, North-Holland, Amsterdam, 1987. | MR | Zbl

[Sa1] M. Sakai, Quadrature Domains, Lecture Notes in Math. Vol. no 934, Springer-Verlag, Berlin-Heidelberg, 1982. | MR | Zbl

[Sa2] M. Sakai, Null quadrature domains, J. Anal. Math. 40 (1981), 144-154. | MR | Zbl

[Sa3] M. Sakai, Regularity of boundary having a Schwarz function, Acta Math. 166 (1991), 263-297. | MR | Zbl

[Sa4] M. Sakai, Regularity of boundaries of quadrature domains in two dimensions, SIAM J. Math. Anal. 24 (1994), 341-364. | MR | Zbl

[Sa5] M. Sakai, Regularity of free boundaries in two dimensions, Ann. Scuola Norm Sup. Pisa Cl. Sci. (4) 20 (1993), 323-339. | Numdam | MR | Zbl

[Sh1] H.S. Shapiro, Unbounded quadrature domains, In: "Complex Analysis I, Proceedings, University of Maryland 1985-86", C.A. Berenstein (ed.), Lecture Notes in Mat., Vol. 1275, Springer-Verlag, 1987, 287-331. | MR | Zbl

[Sh2] H.S. Shapiro, The Schwarz function and Its Generalization to Higher Dimensions, Wiley, New York, University of Arkansas Lecture Notes, 1992. | MR | Zbl

[St] E.M. Stein, Singular Integrals and Differentiability Properties of functions, Princeton University Press, Princeton, 1970. | MR | Zbl

[X] D. Xia, On the kernels associated with a class of hyponormal operators, Integral Equations Operator Theory 6 (1983), 444-452. | MR | Zbl