On p-harmonic functions in the plane and their stream functions

DOI10.1016/0022-0396(88)90022-8zbMath0659.35037OpenAlexW1997961641MaRDI QIDQ1112247

Gunnar Aronsson, Peter Lindqvist

Publication date: 1988

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-0396(88)90022-8

zbMATH Keywords

surveySobolev spacerepresentationanalyticp-harmonic

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Nonlinear elliptic equations (35J60) Biharmonic and polyharmonic equations and functions in higher dimensions (31B30)

Related Items (17)

On Hele–Shaw flow of power-law fluids ⋮ On certain p-harmonic functions in the plane ⋮ Carathéodory operator of differential forms ⋮ On p-harmonic functions in the complex plane and curvature ⋮ Advances in differential forms and the \(A\)-harmonic equation ⋮ Regularity of the \(p\)-Poisson equation in the plane ⋮ Isoperimetric inequalities and regularity of \(a\)-harmonic functions on surfaces ⋮ Thoughts on the Busemann equation ⋮ Representation of a p-harmonic function near a critical point in the plane ⋮ Radó-Kneser-Choquet Theorem for simply connected domains ($p$-harmonic setting) ⋮ Some priori estimates about solutions to nonhomogeneous \(A\)-harmonic equations ⋮ \(p\)-harmonic functions with boundary data having jump discontinuities and Baernstein's problem ⋮ On complex-valued solutions to a 2D Eikonal equation. Part three: analysis of a Bäcklund transformation ⋮ Critical points of solutions of degenerate elliptic equations in the plane ⋮ On \(p\)-harmonic mappings in the plane ⋮ A solution of \(p\)-harmonic type equiations of fractional order ⋮ The streamlines of ∞-harmonic functions obey the inverse mean curvature flow

Cites Work

• Construction of singular solutions to the p-harmonic equation and its limit equation for \(p=\infty\)
• Regularity for a more general class of quasilinear equations
• On solutions of the equation \(D_{x_i}(| Du|^{p-2}D_{x_i}u)=0\) with a singularity at a boundary point
• Capacitary functions in convex rings
• A new proof of local \(C^{1,\alpha}\) regularity for solutions of certain degenerate elliptic P.D.E
• C1 + α local regularity of weak solutions of degenerate elliptic equations
• Analytical foundations of the theory of quasiconformal mappings in R^n
• On The Dirichletproblem for Quasilinear Equations
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