Singular Sets of Higher Order Elliptic Equations

DOI10.1081/PDE-120025495zbMath1290.35065OpenAlexW2073801718MaRDI QIDQ4446128

Qing Han, Fang-Hua Lin, Robert M. Hardt

Publication date: 25 January 2004

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1081/pde-120025495

Mathematics Subject Classification ID

Continuation and prolongation of solutions to PDEs (35B60) Higher-order elliptic equations (35J30)

Related Items (8)

Measure estimates of nodal sets of polyharmonic functions ⋮ Classification of singular sets of solutions to elliptic equations ⋮ Measure upper bounds for nodal sets of eigenfunctions of the bi‐harmonic operator ⋮ Strong unique continuation for the Navier-Stokes equation with non-analytic forcing ⋮ Doubling inequality and nodal sets for solutions of bi-Laplace equations ⋮ Critical sets of solutions to elliptic equations. ⋮ Generic transversality of heteroclinic and homoclinic orbits for scalar parabolic equations ⋮ Nodal sets and horizontal singular sets of ℍ-harmonic functions on the Heisenberg group

Cites Work

• Partial regularity of the zero-set of solutions of linear and superlinear elliptic equations
• Weierstrass-Malgrange preparation theorem in the finitely smooth case
• Local behavior of solutions of general linear elliptic equations
• Geometric measure of singular sets of elliptic equations
• Critical sets of smooth solutions to elliptic equations in dimension 3
• A smooth linear elliptic differential equation without any solution in a sphere
• Schauder estimates for elliptic operators with applications to nodal sets.
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