The Parabolic Infinite-Laplace Equation in Carnot groups [PDF]
, 2014 By employing a Carnot parabolic maximum principle, we show existence-uniqueness of viscosity solutions to a class of equations modeled on the parabolic infinite Laplace equation in Carnot groups.
Bieske, Thomas, Martin, Erin
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Parabolic Biased Infinity Laplacian Equation Related to the Biased Tug-of-War
Advanced Nonlinear Studies, 2019 In this paper, we study the parabolic inhomogeneous β-biased infinity Laplacian equation arising from the β-biased tug-of ...
Liu Fang, Jiang Feida
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Regularity results for the minimum time function with H\"ormander vector fields [PDF]
, 2017 In a bounded domain of $\mathbb{R}^n$ with smooth boundary, we study the regularity of the viscosity solution, $T$, of the Dirichlet problem for the eikonal equation associated with a family of smooth vector fields $\{X_1,\ldots ,X_N\}$, subject to H ...
Albano, Paolo +2 more
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Equivalence of Viscosity and Weak Solutions for the $p(x)$-Laplacian [PDF]
, 2010 We consider different notions of solutions to the $p(x)$-Laplace equation $-\div(\abs{Du(x)}^{p(x)-2}Du(x))=0$ with ...
Acerbi +29 more
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On viscosity and weak solutions for non-homogeneous p-Laplace equations
Advances in Nonlinear Analysis, 2017 In this manuscript, we study the relation between viscosity and weak solutions for non-homogeneous p-Laplace equations with lower-order term depending on x, u and ∇u{\nabla u}.
Medina Maria, Ochoa Pablo
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Solutions of vectorial Hamilton–Jacobi equations are rank-one absolute minimisers in L∞L^{\infty}
Advances in Nonlinear Analysis, 2017 Given the supremal functional E∞(u,Ω′)=esssupΩ′H(⋅,Du){E_{\infty}(u,\Omega^{\prime})=\operatornamewithlimits{ess\,sup}_{\Omega^{% \prime}}H(\,\cdot\,,\mathrm{D}u)}, defined on Wloc1,∞(Ω,ℝN){W^{1,\infty}_{\mathrm{loc}}(\Omega,\mathbb{R}^{N})}, with ...
Katzourakis Nikos
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On cell problems for Hamilton-Jacobi equations with non-coercive Hamiltonians and its application to homogenization problems [PDF]
, 2015 We study a cell problem arising in homogenization for a Hamilton-Jacobi equation whose Hamiltonian is not coercive. We introduce a generalized notion of effective Hamiltonians by approximating the equation and characterize the solvability of the cell ...
Hamamuki, Nao +2 more
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Existence and uniqueness for a crystalline mean curvature flow [PDF]
, 2016 An existence and uniqueness result, up to fattening, for a class of crystalline mean curvature flows with natural mobility is proved. The results are valid in any dimension and for arbitrary, possibly unbounded, initial closed sets.
Almeida +45 more
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The Dirichlet problem for fully nonlinear degenerate elliptic equations with a singular nonlinearity
, 2019 We investigate the homogeneous Dirichlet problem in uniformly convex domains for a large class of degenerate elliptic equations with singular zero order term.
Birindelli, Isabeau, Galise, Giulio
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A comparison among various notions of viscosity solutions for Hamilton-Jacobi equations on networks [PDF]
, 2013 Three definitions of viscosity solutions for Hamilton-Jacobi equations on networks recently appeared in literature ([1,4,6]). Being motivated by various applications, they appear to be considerably different.
Camilli, Fabio, Marchi, Claudio
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