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- W2890556775 abstract "The aim of this paper is to study the heterogeneous optimization problem begin{align*} mathcal {J}(u)=int_{Omega}(G(|nabla u|)+qF(u^+)+hu+lambda_{+}chi_{{u>0}} )text{d}xrightarrowtext{min}, end{align*} in the class of functions $ W^{1,G}(Omega)$ with $ u-varphiin W^{1,G}_{0}(Omega)$, for a given function $varphi$, where $W^{1,G}(Omega)$ is the class of weakly differentiable functions with $int_{Omega}G(|nabla u|)text{d}x<infty$. The functions $G$ and $F$ satisfy structural conditions of Lieberman's type that allow for a different behavior at $0$ and at $infty$. {}{Moreover, $F$ allows for a subcritical growth.} Given functions $q,h$ and constant $lambda_+geq 0$, we address several regularity results for minimizers of $mathcal {J}(u)$, including local $C^{1,alpha}-$, and local Log-Lipschitz continuities for minimizers of $mathcal {J}(u)$ with $lambda_+=0$, and {}{$lambda_+geq 0$} respectively. We also establish growth rate near the free boundary for each non-negative minimizer of $mathcal {J}(u)$ with $lambda_+=0$, and $lambda_+>0$ respectively. Furthermore, under additional assumption that $Fin C^1([0,+infty); [0,+infty))$, local Lipschitz regularity is carried out for non-negative minimizers of $mathcal {J}(u)$ with $lambda_{+}>0$." @default.
- W2890556775 created "2018-09-27" @default.
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- W2890556775 date "2018-09-22" @default.
- W2890556775 modified "2023-09-27" @default.
- W2890556775 title "A minimum problem with free boundary and subcritical growth in Orlicz spaces" @default.
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- W2890556775 doi "https://doi.org/10.48550/arxiv.1809.08518" @default.
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