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- W3103297940 abstract "Given $n in mathbb{N}_*$, a compact Riemannian manifold $M$ and a Sobolev map $u in W^{n/(n + 1), n + 1} (mathbb{S}^n; M)$, we construct a map $U$ in the Sobolev-Marcinkiewicz (or Lorentz-Sobolev) space $W^{1, (n + 1, infty)} (mathbb{B}^{n + 1}; M)$ such that $u = U$ in the sense of traces on $mathbb{S}^{n} = partial mathbb{B}^{n + 1}$ and whose derivative is controlled: for every $lambda > 0$, $$ lambda^{n + 1} bigvertbig{ x in mathbb{B}^{n + 1} : vert D U (x)vert > lambdabig}bigvert le gamma Big(int_{mathbb{S}^n}int_{mathbb{S}^n} frac{vert u (y) - u (z)vert^{n + 1}}{vert y - zvert^{2 n}} ,mathrm{d} y ,mathrm{d} z Bigr) , $$ where the function $gamma : [0, infty) to [0, infty)$ only depends on the dimension $n$ and on the manifold $M$. The construction of the map $U$ relies on a smoothing process by hyperharmonic extension and radial extensions on a suitable covering by balls." @default.
- W3103297940 created "2020-11-23" @default.
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- W3103297940 date "2016-06-27" @default.
- W3103297940 modified "2023-09-27" @default.
- W3103297940 title "Controlled Singular Extension of Critical Trace Sobolev Maps from Spheres to Compact Manifolds" @default.
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- W3103297940 doi "https://doi.org/10.1093/imrn/rnw109" @default.
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