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Complex Variables, Theory and Application: An International Journal Volume 20, 1992 - Issue 1-4
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Original Articles

Singularities encountered by the analytic continuation of solutions to dirichlet's problem

Peter Ebenfelt Department of Mathematics, Royal Institute of Technology, 100 44 Stockholm, Sweden
Pages 75-91 | Received 21 Nov 1991, Published online: 29 May 2007

Citations (16)

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Read on this site (1)

S. R. Bell, P. Ebenfelt, D. Khavinson & H. S. Shapiro. (2007) Algebraicity in the Dirichlet problem in the plane with rational data. Complex Variables and Elliptic Equations 52:2-3, pages 235-244.
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Articles from other publishers (15)

Steven Bell. 2015. The Cauchy Transform, Potential Theory and Conformal Mapping, 2nd Edition. The Cauchy Transform, Potential Theory and Conformal Mapping, 2nd Edition 203 206 .
Steven R. Bell. (2014) The Dirichlet and Neumann and Dirichlet-to-Neumann problems in quadrature, double quadrature, and non-quadrature domains. Analysis and Mathematical Physics 5:2, pages 113-135.
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Steven R. Bell. (2013) An improved Riemann mapping theorem and complexity in potential theory. Arkiv för Matematik 51:2, pages 223-249.
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Hermann Render. (2013) Harmonic divisors and rationality of zeros of Jacobi polynomials. The Ramanujan Journal 31:3, pages 257-270.
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Erik Lundberg & Hermann Render. (2011) The Khavinson–Shapiro conjecture and polynomial decompositions. Journal of Mathematical Analysis and Applications 376:2, pages 506-513.
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Hermann Render. (2010) Cauchy, Goursat and Dirichlet Problems for Holomorphic Partial Differential Equations. Computational Methods and Function Theory 10:2, pages 519-554.
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Erik Lundberg. (2008) Dirichlet’s Problem and Complex Lightning Bolts. Computational Methods and Function Theory 9:1, pages 111-125.
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Hermann Render. (2008) Real Bargmann spaces, Fischer decompositions, and sets of uniqueness for polyharmonic functions. Duke Mathematical Journal 142:2.
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S. R. Bell, P. Ebenfelt, D. Khavinson & H. S. Shapiro. (2006) On the classical Dirichlet problem in the plane with rational data. Journal d’Analyse Mathématique 100:1, pages 157-190.
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Peter Ebenfelt & Michael Viscardi. (2013) On the Solution of the Dirichlet Problem with Rational Holomorphic Boundary Data. Computational Methods and Function Theory 5:2, pages 445-457.
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P. Ebenfelt, D. Khavinson & H.S. Shapiro. 2005. Quadrature Domains and Their Applications. Quadrature Domains and Their Applications 151 172 .
Peter Ebenfelt, Dmitry Khavinson & Harold S. Shapiro. (2013) An Inverse Problem for the Double Layer Potential. Computational Methods and Function Theory 1:2, pages 387-401.
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J. E. McCarthy, E. Yu. Backhaus & J. Fajans. (1998) Solving Poisson’s equation with interior conditions. Journal of Mathematical Physics 39:12, pages 6720-6729.
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Peter Ebenfelt & Harold S. Shapiro. (1995) The mixed Cauchy problem for holomorphic partial differential operators. Journal d'Analyse Mathématique 65:1, pages 237-295.
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Gunnar Johnsson. (1994) The Cauchy problem in 𝐶^{𝑁} for linear second order partial differential equations with data on a quadric surface. Transactions of the American Mathematical Society 344:1, pages 1-48.
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