Harnack's inequality for doubly nonlinear equations of slow diffusion type. [PDF]
Calc Var Partial Differ Equ, 2021 Bögelein V +3 more
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A remark on $C^2$ infinity-harmonic functions
Electronic Journal of Differential Equations, 2006 In this paper, we prove that any nonconstant, $C^2$ solution of the infinity Laplacian equation $u_{x_i}u_{x_j}u_{x_ix_j}=0$ can not have interior critical points. This result was first proved by Aronsson [2] in two dimensions.
Yifeng Yu
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A local singularity analysis for the Ricci flow and its applications to Ricci flows with bounded scalar curvature. [PDF]
Calc Var Partial Differ Equ, 2022 Buzano R, Di Matteo G.
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Harnack inequality for weakly coupled nonlocal systems
In this paper, we consider a weakly coupled system of nonlocal operators which contain both diffusion part with uniformly elliptic diffusion matrices and bounded drift vectors and the jump part with relatively general jump kernels.
Chen, Zhen-Qing, Meng, Xiangqian
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Modeling and multi-objective optimal control of reaction-diffusion COVID-19 system due to vaccination and patient isolation. [PDF]
Appl Math Model, 2023 Tu Y, Hayat T, Hobiny A, Meng X.
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Gradient estimates for a nonlinear parabolic equation with potential under geometric flow
Electronic Journal of Differential Equations, 2015 Let (M,g) be an n dimensional complete Riemannian manifold. In this article we prove local Li-Yau type gradient estimates for all positive solutions to the nonlinear parabolic equation $$ (\partial_t - \Delta_g + \mathcal{R}) u( x, t) = - a u( x, t)
Abimbola Abolarinwa
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Harnack inequality for second order linear ordinary differential inequalities
, 2014 The Harnack Inequality is an important tool in the study of qualitative properties of solutions to elliptic and degenerate elliptic partial differential equations. Perhaps the first paper that discusses such an inequality for ordinary linear differential
Turner, Hannah
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Harnack inequalities for hypoelliptic evolution operators: geometric issues and applications
Bruno Pini Mathematical Analysis Seminar, 2012 We consider linear second order Partial Differential Equations in the form of "sum of squares of Hörmander vector fields plus a drift term" on a given domain.
Sergio Polidoro
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Gradient estimates for a class of elliptic equations with logarithmic terms
Boundary Value ProblemsWe obtain the gradient estimates of the positive solutions to a nonlinear elliptic equation on an n-dimensional complete Riemannian manifold ( M , g ) $(M, g)$ Δ u + a u ( ln u ) p + b u ln u = 0 , $$ \Delta u +au(\ln{u})^{p}+bu\ln{u}=0, $$ where a ≠ 0 ...
Ze Gao, Qiming Guo
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Bruno Pini Mathematical Analysis SeminarLet $\mathcal{L}$ be the hypoelliptic Ornstein-Uhlenbeck operator associated with the pair of matrices (A,B). In 2004, Priola and Zabczyk proved the following Liouville-type theorem: every bounded entire solution of $\mathcal{L}u=0$ is constant if and ...
Alessia E. Kogoj +2 more
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