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A note for W^{1,p}(V) and W_0^{1,p}(V) on a locally finite graph

Autor: Tian, Yulu, Zhao, Liang

In this paper, we investigate the Sobolev spaces W^{1,p}(V) and W_0^{1,p}(V) on a locally finite graph G=(V,E), which are fundamental tools when we apply the variational methods to partial differential equations on graphs. As a key contribution of th

Externí odkaz: http://arxiv.org/abs/2406.08053

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Calculus of variations on hypergraphs

Autor: Shao, Mengqiu, Tian, Yulu, Zhao, Liang

We have established a coherent framework for applying variational methods to partial differential equations on hypergraphs, which includes the propositions of calculus and function spaces on hypergraphs. Several results related to the maximum princip

Externí odkaz: http://arxiv.org/abs/2403.12394

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Generalized Unbiased Scene Graph Generation

Autor: Lyu, Xinyu, Gao, Lianli, Xie, Junlin, Zeng, Pengpeng, Tian, Yulu, Shao, Jie, Shen, Heng Tao

Existing Unbiased Scene Graph Generation (USGG) methods only focus on addressing the predicate-level imbalance that high-frequency classes dominate predictions of rare ones, while overlooking the concept-level imbalance. Actually, even if predicates

Externí odkaz: http://arxiv.org/abs/2308.04802

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Normalized solution to the nonlinear p-Laplacian equation with an L^2 constrain: mass supercritical case

Autor: Tian, Yulu, Wang, Deng-Shan, Zhao, Liang

In this paper, we study the existence of ground state solutions to the following p-Laplacian equation in some dimension $N\geq3$ with an $L^2$ constraint: \begin{equation*} \begin{cases} -\Delta_{p}u+{\vert u\vert}^{p-2}u=f(u)-\mu u \quad \text{ in }

Externí odkaz: http://arxiv.org/abs/2211.01129

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