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- W4387322965 abstract "In this paper, a class of anisotropic weights having the form of $|x'|^{theta_{1}}|x|^{theta_{2}}|x_{n}|^{theta_{3}}$ in dimensions $ngeq2$ is considered, where $x=(x',x_{n})$ and $x'=(x_{1},...,x_{n-1})$. We first find the optimal range of $(theta_{1},theta_{2},theta_{3})$ such that this type of weights belongs to the Muckenhoupt class $A_{q}$. Then we further study its doubling property, which shows that it provides an example of a doubling measure but is not in $A_{q}$. As a consequence, we obtain anisotropic weighted Poincar'{e} and Sobolev inequalities, which are used to study the local behavior for solutions to non-homogeneous weighted $p$-Laplace equations." @default.
- W4387322965 created "2023-10-04" @default.
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- W4387322965 date "2023-10-02" @default.
- W4387322965 modified "2023-10-14" @default.
- W4387322965 title "On a class of anisotropic Muckenhoupt weights and their applications to $p$-Laplace equations" @default.
- W4387322965 doi "https://doi.org/10.48550/arxiv.2310.01359" @default.
- W4387322965 hasPublicationYear "2023" @default.
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