An exponential transform and regularity of free boundaries in two dimensions
Björn Gustafsson; Mihai Putinar
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1998)
- Volume: 26, Issue: 3, page 507-543
- ISSN: 0391-173X
Access Full Article
topHow to cite
topGustafsson, Björn, and Putinar, Mihai. "An exponential transform and regularity of free boundaries in two dimensions." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 26.3 (1998): 507-543. <http://eudml.org/doc/84337>.
@article{Gustafsson1998,
author = {Gustafsson, Björn, Putinar, Mihai},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {free boundary; analytic continuation; Cauchy integral},
language = {eng},
number = {3},
pages = {507-543},
publisher = {Scuola normale superiore},
title = {An exponential transform and regularity of free boundaries in two dimensions},
url = {http://eudml.org/doc/84337},
volume = {26},
year = {1998},
}
TY - JOUR
AU - Gustafsson, Björn
AU - Putinar, Mihai
TI - An exponential transform and regularity of free boundaries in two dimensions
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1998
PB - Scuola normale superiore
VL - 26
IS - 3
SP - 507
EP - 543
LA - eng
KW - free boundary; analytic continuation; Cauchy integral
UR - http://eudml.org/doc/84337
ER -
References
top- [Af] L.V. Ahlfors, Finitely generated Kleinian groups, Amer. J. Math.86 (1964), 413-429. Zbl0133.04201MR167618
- [Ah-Sh] D. Aharonov - H.S. Shapiro, Domains in which analytic functions satisfy quadrature identities, J. Analyse Math. 30 (1976), 39-73. Zbl0337.30029MR447589
- [Be] L. Bers, An approximation theorem, J. Anal. Math.14 (1965), 1-4. Zbl0134.05304MR178287
- [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. Zbl0284.47016MR390830
- [Ca] L. Caffarelli, Compactness methods infree boundary problems, Comm. Partial Differential Equations5 (1980), 427-448. Zbl0437.35070MR567780
- [Cd-Z] A.P. Calderon - A. Zygmund, Local properties of solutions of elliptic partial differential equations, Studia Math.20 (1961), 171-225. Zbl0099.30103MR136849
- [C-Pi] R.W. Carey - J.D. Pincus, An exponential formula for determining functions, Indiana Univ. Math. J.23 (1974), 1031-1042. Zbl0288.47020MR338828
- [Cl1] K. Clancey, A kernel for operators with one-dimensional self-commutator, Integral Equations Operator Theory7 (1984), 441-458. Zbl0585.47024MR757984
- [Cl2] K. Clancey, Hilbert space operators with one-dimensional self-commutator, J. Operator Theory13 (1985), 265-289. Zbl0588.47043MR775998
- [E-G] L.C. Evans - R.F. Gariepy, Measure Theory and Fine Properties of Functions, CRC Press, Boca Raton, 1992. Zbl0804.28001MR1158660
- [D] P.J. Davis, The Schwarz Function and its Applications, Carus Mathematical Monographs, Math. Assoc. Amer., 1974. Zbl0293.30001MR407252
- [Gu1] B. Gustafsson, Quadrature identities and the Schottky double, Acta Appl. Math.1 (1983), 209-240. Zbl0559.30039MR726725
- [Gu2] B. Gustafsson, Singular and special points on quadrature domains from an algebraic geometric point of view, J. Anal. Math.51 (1988), 91-117. Zbl0656.30034MR963151
- [He-Ho] J.W. Helton - R. Howe, Traces of commutators of integral operators, Acta Math.135 (1975), 271-305. Zbl0332.47010MR438188
- [Hm] L. Hörmander, An Introduction to Complex Analysis in Several Variables, North-Holland, Amsterdam, 1989. Zbl0685.32001MR1045639
- [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. Zbl0876.35136MR1444257
- [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. Zbl0361.42014MR458081
- [MP] M. Martin - M. Putinar, Lectures on Hyponormal Operators, Birkhäuser, Basel, 1989. Zbl0684.47018MR1028066
- [Pi] J.D. Pincus, Commutators and systems of singular integral equations I, Acta Math.121 (1968), 219-249. Zbl0179.44601MR240680
- [Pi-Rv] J.D. Pincus - J. Rovnyak, A representation for determining functions, Proc. Amer. Math. Soc.22 (1969), 498-502. Zbl0188.42801MR248569
- [P1] M. Putinar, Extremal solutions of the two-dimensional L-problem of moments, J. Funct. Anal. 136 (1996), 331-364. Zbl0917.47014MR1380658
- [P2] M. Putinar, Linear analysis of quadrature domains, Ark. Mat.33 (1995), 357-376. Zbl0892.47025MR1373029
- [P3] M. Putinar, Extremal solutions of the two-dimensional L-problem of moments II, J. Approx. Theory (to appear). Zbl0910.47011MR1492857
- [Re] Yu G. Reshetnyak, Generalized derivatives and differentiability almost everywhere, Mat. Sb.75 (1968), 323-334 (translated from Russian). Zbl0165.47202MR225159
- [Ro] J.F. Rodrigues, Obstacle Problems in Mathematical Physics, North-Holland, Amsterdam, 1987. Zbl0606.73017MR880369
- [Sa1] M. Sakai, Quadrature Domains, Lecture Notes in Math. Vol. no 934, Springer-Verlag, Berlin-Heidelberg, 1982. Zbl0483.30001MR663007
- [Sa2] M. Sakai, Null quadrature domains, J. Anal. Math.40 (1981), 144-154. Zbl0483.30002MR659788
- [Sa3] M. Sakai, Regularity of boundary having a Schwarz function, Acta Math.166 (1991), 263-297. Zbl0728.30007MR1097025
- [Sa4] M. Sakai, Regularity of boundaries of quadrature domains in two dimensions, SIAM J. Math. Anal.24 (1994), 341-364. Zbl0771.30041MR1205531
- [Sa5] M. Sakai, Regularity of free boundaries in two dimensions, Ann. Scuola Norm Sup. Pisa Cl. Sci. (4) 20 (1993), 323-339. Zbl0851.35022MR1256071
- [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. Zbl0634.30037MR922309
- [Sh2] H.S. Shapiro, The Schwarz function and Its Generalization to Higher Dimensions, Wiley, New York, University of Arkansas Lecture Notes, 1992. Zbl0784.30036MR1160990
- [St] E.M. Stein, Singular Integrals and Differentiability Properties of functions, Princeton University Press, Princeton, 1970. Zbl0207.13501MR290095
- [X] D. Xia, On the kernels associated with a class of hyponormal operators, Integral Equations Operator Theory6 (1983), 444-452. Zbl0554.47009MR701029
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.