Explicit infty-harmonic functions in high dimensions
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🧮 math.AP
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inftydimensionsexplicitfunctionssolutionsalreadyarbitraryarising
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The aim of this work is to derive new explicit solutions to the $\infty$-Laplace equation, the fundamental PDE arising in Calculus of Variations in the space $L^\infty$. These solutions obey certain symmetry conditions and are derived in arbitrary dimensions, containing as particular sub-cases the already known classes two-dimensional infinity-harmonic functions.
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