Cauchy, Goursat and Dirichlet problems for holomorphic partial differential equations

DOI10.1007/BF03321779zbMath1207.35013OpenAlexW2037865664MaRDI QIDQ619444

Hermann Render

Publication date: 25 January 2011

Published in: Computational Methods and Function Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf03321779

zbMATH Keywords

Dirichlet problemCauchy problempolyharmonic functionGoursat problemJacobi polynomialFischer decompositionholomorphic PDEKhavinson-Shapiro conjecture

Mathematics Subject Classification ID

Biharmonic and polyharmonic equations and functions in higher dimensions (31B30) Analyticity in context of PDEs (35A20) Cauchy-Kovalevskaya theorems (35A10)

Related Items (5)

Positivity properties for the clamped plate boundary problem on the ellipse and strip ⋮ The Khavinson-Shapiro conjecture and the Bergman projection in one and several complex variables ⋮ On polyharmonic polynomials ⋮ Dirichlet's problem with entire data posed on an ellipsoidal cylinder ⋮ Pseudo-differential operators with meromorphic symbols and systems of complex differential equations

Cites Work

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• Harmonic divisors and rationality of zeros of Jacobi polynomials
• The Khavinson-Shapiro conjecture and polynomial decompositions
• The Dirichlet problem for the wave equation
• The Goursat problem for a generalized Helmholtz operator in the plane
• On the classical Dirichlet problem in the plane with rational data
• Spectral property of Goursat problems
• Representation and uniqueness theorems for polyharmonic functions
• A quasi maximum principle for holomorphic solutions of partial differential equations in \(\mathbb{C}^ n\)
• Cases when the solution of the Dirichlet problem for the Laplace equation on a polygon is a polynomial.
• The Dirichlet problem when the boundary function is entire
• The case where a solution to a boundary-value problem is a polynomial
• On the Dirichlet problem for the nonlinear wave equation in bounded domains with corner points
• Caractere non fredholmien du problème de Goursat
• Geometry of stationary sets for the wave equation in \(\mathbb R^n\): the case of finitely supported initial data
• The mixed Cauchy problem for holomorphic partial differential operators
• A boundary value problem for the wave equation
• On a property of solutions to the Poisson equation on polygons
• Poincaré's variational problem in potential theory
• Dirichlet's problem and complex lightning bolts
• Some aspects of the nontrivial solvability of homogeneous Dirichlet problems for linear equations of arbitrary even order in the disk
• Polynomials orthogonal over a curve
• Finite-term relations for planar orthogonal polynomials
• Real Bargmann spaces, Fischer decompositions, and sets of uniqueness for polyharmonic functions
• On the solution of the Dirichlet problem with rational holomorphic boundary data
• Une variante de la méthode de majoration de Cauchy
• The condition for uniqueness of solutions of the Dirichlet problem for the wave equation in coordinate rectangles
• Irreducibility of certain classes of Legendre polynomials
• New cases of irreducibility for Legendre polynomials. II
• On the local and global non-characteristic Cauchy problem when the solutions are holomorphic functions or analytic functionals in the space variables
• The Dirichlet problem for the damped wave equation
• New cases of irreducibility for Legendre polynomials
• Harmonic Function Theory
• The Dirichlet Problem for Ellipsoids
• On a Hilbert space of analytic functions and an associated integral transform part I
• Singularities encountered by the analytic continuation of solutions to dirichlet's problem
• Algebraicity in the Dirichlet problem in the plane with rational data
• An Algebraic Theorem of E. Fischer, and the Holomorphic Goursat Problem
• On the mixed Cauchy problem with data on singular conics
• Problèmes de Cauchy globaux
• Dirichlet's Problem When the Data is an Entire Function
• Conical Uniqueness Sets for the Spherical Radon Transform
• Functional equations and harmonic extensions
• The Cauchy Problem in ℂ N for Linear Second Order Partial Differential Equations with Data on a Quadric Surface
• Cauchy’s Problem for Harmonic Functions with Entire Data on a Sphere
• The Dirichlet problem on quadratic surfaces
• Polynomial solutions to Dirichlet problems
• The cauchy-kowalevskaya theorem and generalizations
• Harmonic Polynomials and Dirichlet-Type Problems
• Equivalence of Cauchy Problems for Entire and Exponential Type Functions
• Recurrence Relations for Orthogonal Polynomials and Algebraicity of Solutions of the Dirichlet Problem
• The Level Curves of Harmonic Functions
• A Poisson Integral Formula for the Ellipse and Some Applications
• Certain Hilbert spaces of entire functions
• Uniqueness of Solutions of the Dirichlet and Neumann Problems for Hyperbolic Equations
• A New Proof and Generalizations of the Cauchy-Kowalewski Theorem
• The Dirichlet problem for the vibrating string equation
• The Dirichlet Problem for a Hyperbolic Equation
• The Harmonic Boundary Value Problem for an Ellipse or an Ellipsoid
• On the solvability of Goursat problems and a function of number theory
• Quadratic divisors of harmonic polynomials in \(\mathbb{R}^n\)

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