On the uniqueness theorem of Holmgren

DOI10.1007/s00209-015-1488-6zbMath1329.35009arXiv1312.4348OpenAlexW2143758652WikidataQ59288358 ScholiaQ59288358MaRDI QIDQ495587

Haakan Hedenmalm

Publication date: 14 September 2015

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.4348

zbMATH Keywords

Dirichlet problemCauchy problemHolmgren's uniqueness theorem

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Cauchy-Kovalevskaya theorems (35A10) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

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Cites Work

• Weighted integrability of polyharmonic functions
• Differential operators for a scale of Poisson type kernels in the unit disc
• Counterexamples to Hölmgren's uniqueness for analytic nonlinear Cauchy problems
• Regularity of a boundary having a Schwarz function
• Domains on which analytic functions satisfy quadrature identities
• Remarks on Holmgren's uniqueness theorem
• The analysis of linear partial differential operators. II: Differential operators with constant coefficients
• Uniqueness and free interpolation for logarithmic potentials and the Cauchy problem for the Laplace equation in \(\mathbb{R}^ 2\)
• A remark on gradients of harmonic functions
• Quadrature identities and the Schottky double
• On the non-vanishing of the Jacobian of a homeomorphism by harmonic gradients
• Off-critical lattice models and massive SLEs
• A remark on gradients of harmonic functions in dimension ≥3
• Generalized axially symmetric potential theory
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