Li–Yau-Type Gradient Estimate along Geometric Flow
Mathematics, 2023 In this article we derive a Li–Yau-type gradient estimate for a generalized weighted parabolic heat equation with potential on a weighted Riemannian manifold evolving by a geometric flow.
Shyamal Kumar Hui +5 more
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Gradient estimate of the solutions to Hessian equations with oblique boundary value
Advanced Nonlinear Studies, 2022 In this paper, we study Hessian equations with the prescribed contact angle boundary value or oblique derivative boundary value and finally derive the a priori global gradient estimate for the admissible solutions.
Wang PeiHe
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Singular quasilinear convective systems involving variable exponents [PDF]
Opuscula Mathematica, 2023 The paper deals with the existence of solutions for quasilinear elliptic systems involving singular and convection terms with variable exponents. The approach combines the sub-supersolutions method and Schauder's fixed point theorem.
Abdelkrim Moussaoui +2 more
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Harnack Estimation for Nonlinear, Weighted, Heat-Type Equation along Geometric Flow and Applications
Mathematics, 2023 The method of gradient estimation for the heat-type equation using the Harnack quantity is a classical approach used for understanding the nature of the solution of these heat-type equations. Most of the studies in this field involve the Laplace–Beltrami
Yanlin Li +4 more
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Deep Learning-Based Algorithm for Recognizing Tennis Balls
Applied Sciences, 2022 In this paper, we adjust the hyperparameters of the training model based on the gradient estimation theory and optimize the structure of the model based on the loss function theory of Mask R-CNN convolutional network and propose a scheme to help a tennis
Di Wu, Aiping Xiao
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Global gradient estimates for Dirichlet problems of elliptic operators with a BMO antisymmetric part
Advances in Nonlinear Analysis, 2022 Let n≥2n\ge 2 and Ω⊂Rn\Omega \subset {{\mathbb{R}}}^{n} be a bounded nontangentially accessible domain. In this article, the authors investigate (weighted) global gradient estimates for Dirichlet boundary value problems of second-order elliptic equations
Yang Sibei, Yang Dachun, Yuan Wen
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Lipschitz Continuity for Harmonic Functions and Solutions of the
Axioms, 2023 In this paper we investigate the solutions of the so-called α¯-Poisson equation in the complex plane. In particular, we will give sufficient conditions for Lipschitz continuity of such solutions. We also review some recently obtained results.
Miodrag Mateljević +2 more
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CDE’ Inequality on Graphs with Unbounded Laplacian
Mathematics, 2023 In this paper, we derive the gradient estimates of semigroups in terms of the modified curvature-dimension inequality CDE′ for unbounded Laplacians on complete graphs with non-degenerate measures.
Desheng Hong, Chao Gong
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The exterior Dirichlet problem for the homogeneous complex k-Hessian equation
Advanced Nonlinear Studies, 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.
Gao Zhenghuan, Ma Xinan, Zhang Dekai
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Gradient Profile Estimation Using Exponential Cubic Spline Smoothing in a Bayesian Framework
Entropy, 2021 Attaining reliable gradient profiles is of utmost relevance for many physical systems. In many situations, the estimation of the gradient is inaccurate due to noise.
Kushani De Silva +2 more
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