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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Short time behaviour for game-theoretic $p$-caloric functions [PDF]
, 2018 We consider the solution of $u_t-\Delta^G_p u=0$ in a (not necessarily bounded) domain, satisfying $u=0$ initially and $u=1$ on the boundary at all times. Here, $\Delta^G_p u$ is the game-theoretic or normalized $p$-laplacian.
Berti, Diego, Magnanini, Rolando
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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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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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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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CLASSIFICATION OF EXTINCTION PROFILES FOR A ONE-DIMENSIONAL DIFFUSIVE HAMILTON-JACOBI EQUATION WITH CRITICAL ABSORPTION [PDF]
, 2018 International audienceA classification of the behavior of the solutions f (·, a) to the ordinary differential equation (|f ′ |^{p−2} f ′) ′ + f − |f ′ |^{p−1} = 0 in (0, ∞) with initial condition f (0, a) = a and f ′ (0, a) = 0 is provided, according to ...
Iagar, Razvan,, Laurençot, Philippe
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Existence of weak solutions for a PDE system describing phase separation and damage processes including inertial effects [PDF]
, 2014 In this paper, we consider a coupled PDE system describing phase separation and damage phenomena in elastically stressed alloys in the presence of inertial effects.
Heinemann, Christian, Kraus, Christiane
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Evolutionary quasi-variational and variational inequalities with constraints on the derivatives
Advances in Nonlinear Analysis, 2018 This paper considers a general framework for the study of the existence of quasi-variational and variational solutions to a class of nonlinear evolution systems in convex sets of Banach spaces describing constraints on a linear combination of partial ...
Miranda Fernando +2 more
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Ireneo Peral: Forty Years as Mentor
Advanced Nonlinear Studies, 2017 In this article we present a survey of the Ph.D. theses that have been completed under the advice of Ireneo Peral.Following a chronological order, we summarize the main results contained in the works of the former students of Ireneo Peral.
Abdellaoui Boumediene +9 more
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