Solutions with high dimensional singular set, to a conformally invariant elliptic equation in ℝ4 and in ℝ6

Frank Pacard

doi:10.1007/BF02102645

Solutions with high dimensional singular set, to a conformally invariant elliptic equation in ℝ⁴ and in ℝ⁶

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Abstract

We construct positive weak solutions to the equation {Mathematical expression}, where -Δ₀ denotes the conformal Laplacian on the n-sphere (n=4, 6), having singular sets of Hausdorff dimension greater than or equal to {Mathematical expression}.

Original language	English
Pages (from-to)	423-432
Number of pages	10
Journal	Communications in Mathematical Physics
Volume	159
Issue number	2
DOIs	https://doi.org/10.1007/BF02102645
Publication status	Published - 1 Jan 1994

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title = "Solutions with high dimensional singular set, to a conformally invariant elliptic equation in ℝ4 and in ℝ6",

abstract = "We construct positive weak solutions to the equation \{Mathematical expression\}, where -Δ0 denotes the conformal Laplacian on the n-sphere (n=4, 6), having singular sets of Hausdorff dimension greater than or equal to \{Mathematical expression\}.",

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year = "1994",

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AB - We construct positive weak solutions to the equation {Mathematical expression}, where -Δ0 denotes the conformal Laplacian on the n-sphere (n=4, 6), having singular sets of Hausdorff dimension greater than or equal to {Mathematical expression}.

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JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

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Solutions with high dimensional singular set, to a conformally invariant elliptic equation in ℝ4 and in ℝ6

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Solutions with high dimensional singular set, to a conformally invariant elliptic equation in ℝ⁴ and in ℝ⁶