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- W4386363485 abstract "We construct and analyze solutions to a regularized homogeneous $p$-harmonic map flow equation for general $p geq 2$. The homogeneous version of the problem is new and features a monotonicity formula extending the one found by Struwe for $p = 2$; such a formula is not available for the nonhomogeneous equation. The construction itself is via a Ginzburg-Landau-type approximation `a la Chen-Struwe, employing tools such as a Bochner-type formula and an $varepsilon$-regularity theorem. We similarly obtain strong subsequential convergence of the approximations away from a concentration set with parabolic codimension at least $p$. However, the quasilinear and non-divergence nature of the equation presents new obstacles that do not appear in the classical case $p = 2$, namely uniform-time existence for the approximating problem, and thus our basic existence result is stated conditionally." @default.
- W4386363485 created "2023-09-02" @default.
- W4386363485 creator A5088671856 @default.
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- W4386363485 date "2023-08-30" @default.
- W4386363485 modified "2023-09-27" @default.
- W4386363485 title "A new $p$-harmonic map flow with Struwe monotonicity" @default.
- W4386363485 doi "https://doi.org/10.48550/arxiv.2308.16096" @default.
- W4386363485 hasPublicationYear "2023" @default.
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