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arXiv · 2309.07417

On the singular problem involving $g$-Laplacian

Kaushik Bal·Riddhi Mishra·Kaushik Mohanta
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Abstract

In this paper, we show that the existence of a positive weak solution to the equation $(-\Delta_g)^s u=f u^{-q(x)}\;\mbox{in}\; \Omega,$ where $\Omega$ is a smooth bounded domain in $R^N$, $q\in C^1(\overline{\Omega})$, and $(-\Delta_g)^s$ is the fractional $g$-Laplacian with $g$ is the antiderivative of a Young function and $f$ in suitable Orlicz space subjected to zero Dirichlet condition. This includes the mixed fractional $(p,q)-$Laplacian as a special case. The solution so obtained is also shown to be locally H\"older continuous.

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Kaushik Bal, Riddhi Mishra, Kaushik Mohanta. 2023-09-14. On the singular problem involving $g$-Laplacian. https://arxiv.org/abs/2309.07417

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