Liouville theorem for Dunkl polyharmonic functions.

Ren, Guangbin; Liu, Liang

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Radial limits of superharmonic functions in the plane

D. Armitage (1994)

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Fischer decompositions in Euclidean and Hermitean Clifford analysis

Freddy Brackx, Hennie de Schepper, Vladimír Souček (2010)

Archivum Mathematicum

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Euclidean Clifford analysis is a higher dimensional function theory studying so–called monogenic functions, i.e. null solutions of the rotation invariant, vector valued, first order Dirac operator $\underset{̲}{\partial}$ . In the more recent branch Hermitean Clifford analysis, this rotational invariance has been broken by introducing a complex structure $J$ on Euclidean space and a corresponding second Dirac operator ${\underset{̲}{\partial}}_{J}$ , leading to the system of equations $\underset{̲}{\partial} f = 0 = {\underset{̲}{\partial}}_{J} f$ expressing so-called Hermitean monogenicity. The invariance...

A note on non-negative singular infinity-harmonic functions in the half-space.

Tilak Bhattacharya (2005)

Revista Matemática Complutense

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In this work we study non-negative singular infinity-harmonic functions in the half-space. We assume that solutions blow-up at the origin while vanishing at infinity and on a hyperplane. We show that blow-up rate is of the order |x|.