On the fatou theorem for p-harmonic function

DOI10.1080/03605308808820556zbMath0661.31014OpenAlexW2079588586MaRDI QIDQ3810096

Allen Weitsman, Juan J. Manfredi

Publication date: 1988

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

Full work available at URL: https://doi.org/10.1080/03605308808820556

zbMATH Keywords

existencediscontinuous coefficientsHausdorff dimensionkernel functionboundary valuesCordes conditionp-Laplace equationp-harmonicnon-negative weak solutionsL-harmonic measureradial boundary limits

Mathematics Subject Classification ID

Second-order elliptic equations (35J15) Boundary values of solutions to elliptic equations and elliptic systems (35J67) Integral representations, integral operators, integral equations methods in higher dimensions (31B10) Boundary behavior of harmonic functions in higher dimensions (31B25)

Related Items (21)

Fatou theorem of \(p\)-harmonic functions on trees. ⋮ On a linearized \(p\)-Laplace equation with rapidly oscillating coefficients ⋮ Differentiability of solutions for the non-degenerate \(p\)-Laplacian in the Heisenberg group ⋮ On a theorem of Wolff revisited ⋮ The regularity of solutions to some variational problems, including the \(p\)-Laplace equation for \(3\leq p < 4\) ⋮ Unnamed Item ⋮ Traces of monotone Sobolev functions ⋮ Hessian estimates for equations involving \(p\)-Laplacian via a fundamental inequality ⋮ A second-order Sobolev regularity for \(p(x)\)-Laplace equations ⋮ A quantitative second order estimate for (weighted) \(p\)-harmonic functions in manifolds under curvature-dimension condition ⋮ Isoperimetric inequalities and regularity of \(a\)-harmonic functions on surfaces ⋮ \(\mathrm{HW}^{2, 2}_\mathrm{loc}\)-regularity for \(p\)-harmonic functions in Heisenberg groups ⋮ Fractional differentiability for solutions of the inhomogeneous 𝑝-Laplace system ⋮ An index formula for elliptic systems in the plane ⋮ A boundary Harnack principle for infinity-Laplacian and some related results ⋮ Remarks on regularity for \(p\)-Laplacian type equations in non-divergence form ⋮ Boundary Harnack inequality and a priori estimates of singular solutions of quasilinear elliptic equations ⋮ Unnamed Item ⋮ Global second order Sobolev-regularity of \(p\)-harmonic functions ⋮ Note on an elementary inequality and its application to the regularity of p-harmonic functions ⋮ On the second-order regularity of solutions to the parabolic \(p\)-Laplace equation

Cites Work

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• Positive solutions of elliptic equations in nondivergence form and their adjoints
• Boundary behavior of harmonic functions in non-tangentially accessible domains
• A new proof of local \(C^{1,\alpha}\) regularity for solutions of certain degenerate elliptic P.D.E
• Gap series constructions for the \(p\)-Laplacian
• Sopra una classe di equazioni ellittiche a coefficienti misurabili
• Barriers on cones for uniformly elliptic operators
• Operatori ellittice estremanti

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