Zobrazeno 1 - 10
of 270
pro vyhledávání: '"ZHANG DEKAI"'
Publikováno v:
Advanced Nonlinear Studies, Vol 23, Iss 1, Pp 51-85 (2023)
In this article, we consider the homogeneous complex kk-Hessian equation in an exterior domain Cn⧹Ω{{\mathbb{C}}}^{n}\setminus \Omega . We prove the existence and uniqueness of the C1,1{C}^{1,1} solution by constructing approximating solutions. Th
Externí odkaz:
https://doaj.org/article/ba2a4ae044854094a9a3625bb584ab86
Autor:
Zhang Dekai
Publikováno v:
Advanced Nonlinear Studies, Vol 22, Iss 1, Pp 534-547 (2022)
In this article, we are concerned with the existence of weak C1,1{C}^{1,1} solution of the kk-Hessian equation on a closed Hermitian manifold under the optimal assumption of the function in the right-hand side of the equation. The key points are to s
Externí odkaz:
https://doaj.org/article/909baf8522664f848e7be174c7f390f8
Autor:
Leofante, Francesco, Ayoobi, Hamed, Dejl, Adam, Freedman, Gabriel, Gorur, Deniz, Jiang, Junqi, Paulino-Passos, Guilherme, Rago, Antonio, Rapberger, Anna, Russo, Fabrizio, Yin, Xiang, Zhang, Dekai, Toni, Francesca
AI has become pervasive in recent years, but state-of-the-art approaches predominantly neglect the need for AI systems to be contestable. Instead, contestability is advocated by AI guidelines (e.g. by the OECD) and regulation of automated decision-ma
Externí odkaz:
http://arxiv.org/abs/2405.10729
Autor:
Qiu, Guohuan, Zhang, Dekai
We study the Neumann problem for special Lagrangian type equations with critical and supercritical phases. These equations naturally generalize the special Lagrangian equation and the k-Hessian equation. By establishing uniform a priori estimates up
Externí odkaz:
http://arxiv.org/abs/2403.06110
We prove the long time existence and uniqueness of solution to a parabolic quaternionic Monge-Amp\`{e}re type equation on a compact hyperK\"{a}hler manifold. We also show that after normalization, the solution converges smoothly to the unique solutio
Externí odkaz:
http://arxiv.org/abs/2310.09225
Neural networks (NNs) can learn to rely on spurious signals in the training data, leading to poor generalisation. Recent methods tackle this problem by training NNs with additional ground-truth annotations of such signals. These methods may, however,
Externí odkaz:
http://arxiv.org/abs/2311.12813
In this paper, we consider the homogeneous complex k-Hessian equation in $\Omega\backslash\{0\}$. We prove the existence and uniqueness of the $C^{1,\alpha}$ solution by constructing approximating solutions. The key point for us is to construct the s
Externí odkaz:
http://arxiv.org/abs/2304.08407
In this paper, we consider the Dirichlet problem for the homogeneous $k$-Hessian equation with prescribed asymptotic behavior at $0\in\Omega$ where $\Omega$ is a $(k-1)$-convex bounded domain in the Euclidean space. The prescribed asymptotic behavior
Externí odkaz:
http://arxiv.org/abs/2303.07976
We prove the existence of unique smooth solutions to the quaternionic Monge-Amp\`{e}re equation for $(n-1)$-quaternionic plurisubharmonic functions on a hyperK\"{a}hler manifold and thus obtain solutions for the quaternionic form type equation. We de
Externí odkaz:
http://arxiv.org/abs/2301.09119
We prove the symmetry of solutions to overdetermined problems for a class of fully nonlinear equations, namely Hessian quotient equations and Hessian quotient curvature equations. Our approach is based on establishing a Rellich-Pohozaev type identity
Externí odkaz:
http://arxiv.org/abs/2209.06268