Displaying similar documents to “Regularity of p-harmonic functions on the plane.”

On pseudospheres that are quasispheres.

John L. Lewis, Andrew Vogel (2001)

Revista Matemática Iberoamericana

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We construct bounded domains D not equal to a ball in n ≥ 3 dimensional Euclidean space, R, for which ∂D is homeomorphic to a sphere under a quasiconformal mapping of R and such that n - 1 dimensional Hausdorff measure equals harmonic measure on ∂D.

Quasimonotone systems of higher order

Manfred Kronz (2003)

Bollettino dell'Unione Matematica Italiana

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We consider higher order quasimonotone nonlinear systems of divergence type with growth of order p , p ≥ 2 , and Dini continuous coefficients. Using the technique of harmonic approximation we give a direct partial regularity proof for weak solutions.

«Approximate approximations» and the cubature of potentials

Gunther Schmidt (1995)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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The paper discusses new cubature formulas for classical integral operators of mathematical physics based on the «approximate approximation» of the density with Gaussian and related functions. We derive formulas for the cubature of harmonic, elastic and diffraction potentials approximating with high order in some range relevant for numerical computations. We prove error estimates and provide numerical results for the Newton potential.