We extend the weighted gradient estimate for solutions of nonlinear PDE associated to the prescribed $ k $-th $ L^p $-area measure problem to the case $ 0 < p < 1 $. The estimate yields non-collapsing estimate for symmetric convex bodied with prescribed $ L^p $-area measures.
Citation: Pengfei Guan. A weighted gradient estimate for solutions of $ L^p $ Christoffel-Minkowski problem[J]. Mathematics in Engineering, 2023, 5(3): 1-14. doi: 10.3934/mine.2023067
We extend the weighted gradient estimate for solutions of nonlinear PDE associated to the prescribed $ k $-th $ L^p $-area measure problem to the case $ 0 < p < 1 $. The estimate yields non-collapsing estimate for symmetric convex bodied with prescribed $ L^p $-area measures.
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Pengfei Guan. A weighted gradient estimate for solutions of $ L^p $ Christoffel-Minkowski problem[J]. Mathematics in Engineering, 2023, 5(3): 1-14. doi: 10.3934/mine.2023067
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