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- W2912128947 abstract "We prove an analogue of Wolff's inequality for the so-called intrinsic nonlinear potentials associated with the quasilinear elliptic equation [ -Delta_{p} u = sigma u^{q} quad text{in} ;; mathbb{R}^n, ] in the sub-natural growth case $0<q< p-1$, where $Delta_{p}u = text{div}( |nabla u|^{p-2} nabla u )$ is the $p$-Laplacian, and $sigma$ is a nonnegative measurable function (or measure) on $mathbb{R}^n$. As an application, we give a necessary and sufficient condition for the existence of a positive solution $u in L^{r}(mathbb{R}^{n})$ ($0<r<infty$) to this problem, which was open even in the case $p=2$. Our version of Wolff's inequality for intrinsic nonlinear potentials relies on a new characterization of discrete Littlewood-Paley spaces $f^{p, q}(sigma)$ defined in terms of characteristic functions of dyadic cubes in $mathbb{R}^n$." @default.
- W2912128947 created "2019-02-21" @default.
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- W2912128947 date "2018-12-09" @default.
- W2912128947 modified "2023-09-27" @default.
- W2912128947 title "Wolff's inequality for intrinsic nonlinear potentials and quasilinear elliptic equations" @default.
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