In this brief note we show that under a volume non-preserving scaling it is possible to recover the basics for a regularity theory regarding local weak solutions to the fully anisotropic equation 1∂tu=∑i=1N∂i(|∂iu|pi−2∂iu)inΩT=Ω×(−T,T),withΩ⊂⊂ℝN.We characterize self-similar solutions regarding this particular scaling and we show that semi-continuity for solutions to this equation is a consequence of a simple property that is itself invariant under scaling.
Ciani, S., Guarnotta, U., Vespri, V. (2023). On a Particular Scaling for the Prototype Anisotropic p-Laplacian. Cham : Birkhäuser [10.1007/978-3-031-20021-2_15].
On a Particular Scaling for the Prototype Anisotropic p-Laplacian
Ciani, Simone
;Vespri, Vincenzo
2023
Abstract
In this brief note we show that under a volume non-preserving scaling it is possible to recover the basics for a regularity theory regarding local weak solutions to the fully anisotropic equation 1∂tu=∑i=1N∂i(|∂iu|pi−2∂iu)inΩT=Ω×(−T,T),withΩ⊂⊂ℝN.We characterize self-similar solutions regarding this particular scaling and we show that semi-continuity for solutions to this equation is a consequence of a simple property that is itself invariant under scaling.File in questo prodotto:
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