Hölder gradient estimates for a class of singular or degenerate parabolic equations
Advances in Nonlinear Analysis, 2017 We prove interior Hölder estimates for the spatial gradients of the viscosity solutions to the singular or degenerate parabolic ...
Imbert Cyril +2 more
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Advanced Nonlinear Studies, 2021 The purpose of the article is to study the existence, regularity, stabilization and blow-up results of weak solution to the following parabolic (p,q){(p,q)}-singular equation:
Giacomoni Jacques +2 more
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Blow-up results of the positive solution for a class of degenerate parabolic equations
Open Mathematics, 2021 This paper is devoted to discussing the blow-up problem of the positive solution of the following degenerate parabolic equations: (r(u))t=div(∣∇u∣p∇u)+f(x,t,u,∣∇u∣2),(x,t)∈D×(0,T∗),∂u∂ν+σu=0,(x,t)∈∂D×(0,T∗),u(x,0)=u0(x),x∈D¯.\left\{\begin{array}{ll}{(r ...
Dong Chenyu, Ding Juntang
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On the local behavior of local weak solutions to some singular anisotropic elliptic equations
Advances in Nonlinear Analysis, 2022 We study the local behavior of bounded local weak solutions to a class of anisotropic singular equations of the kind ∑i=1s∂iiu+∑i=s+1N∂i(Ai(x,u,∇u))=0,x∈Ω⊂⊂RNfor1≤s≤(N−1),\mathop{\sum }\limits_{i=1}^{s}{\partial }_{ii}u+\mathop{\sum }\limits_{i=s+1}^{N}{\
Ciani Simone +2 more
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On a final value problem for a nonhomogeneous fractional pseudo-parabolic equation
Alexandria Engineering Journal, 2020 In this paper, we are interested in finding the function u(t,x),(t,x)∈[0,T)×Ω from the final data u(T,x)=ϕ(x), satisfies a nonhomogeneous fractional pseudo-parabolic equation. The problem is stable for the cases σν, the problem is ill-posed (in the sense
Nguyen Hoang Luc +3 more
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A local estimate for vectorial total variation minimization in one dimension [PDF]
, 2018 Let $\boldsymbol u$ be the minimizer of vectorial total variation ($VTV$) with $L^2$ data-fidelity term on an interval $I$. We show that the total variation of $\boldsymbol u$ over any subinterval of $I$ is bounded by that of the datum over the same ...
Giacomelli, Lorenzo, Łasica, Michał
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A conditional regularity result for p-harmonic flows [PDF]
, 2015 We prove an $\varepsilon$-regularity result for a wide class of parabolic systems $$ u_t-\text{div}\big(|\nabla u|^{p-2}\nabla u) = B(u, \nabla u) $$ with the right hand side $B$ growing like $|\nabla u|^p$.
Katarzyna Ewa Mazowiecka +4 more
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Parabolic BMO and global integrability of supersolutions to doubly nonlinear parabolic equations [PDF]
, 2015 We prove that local and global parabolic BMO spaces are equal thus extending the classical result of Reimann and Rychener. Moreover, we show that functions in parabolic BMO are exponentially integrable in a general class of space-time cylinders.
Saari, Olli
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A natural approach to the asymptotic mean value property for the $p$-Laplacian [PDF]
, 2016 Let $1\le p\le\infty$. We show that a function $u\in C(\mathbb R^N)$ is a viscosity solution to the normalized $p$-Laplace equation $\Delta_p^n u(x)=0$ if and only if the asymptotic formula $$ u(x)=\mu_p(\ve,u)(x)+o(\ve^2) $$ holds as $\ve\to 0$ in the ...
Ishiwata, Michinori +2 more
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Modeling and analysis of a phase field system for damage and phase separation processes in solids [PDF]
, 2013 In this work, we analytically investigate a multi-component system for describing phase separation and damage processes in solids. The model consists of a parabolic diffusion equation of fourth order for the concentration coupled with an elliptic system ...
Bonetti, Elena +3 more
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