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A large scaling property of level sets for degenerate p$p$‐Laplacian equations with logarithmic BMO matrix weights

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  • Thanh‐Nhan Nguyen
  • Minh‐Phuong Tran

Abstract

In this study, we deal with generalized regularity properties for solutions to p$p$‐Laplace equations with degenerate matrix weights. It has been already observed in previous interesting works that gaining Calderón–Zygmund estimates for nonlinear equations with degenerate weights under the so‐called log-BMO$\log\text{-}\mathrm{BMO}$ condition and minimal regularity assumption on the boundary. In this paper, we also follow this direction and extend general gradient estimates for level sets of the gradient of solutions up to more subtle function spaces. In particular, we construct a covering of the super‐level sets of the spatial gradient |∇u|$|\nabla u|$ with respect to a large scaling parameter via fractional maximal operators.

Suggested Citation

  • Thanh‐Nhan Nguyen & Minh‐Phuong Tran, 2025. "A large scaling property of level sets for degenerate p$p$‐Laplacian equations with logarithmic BMO matrix weights," Mathematische Nachrichten, Wiley Blackwell, vol. 298(10), pages 3287-3306, October.
  • Handle: RePEc:bla:mathna:v:298:y:2025:i:10:p:3287-3306
    DOI: 10.1002/mana.70039
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