Encontrados 26 documentos, a visualizar página 1 de 3
Local Hölder continuity for doubly nonlinear parabolic equations
Kuusi, Tuomo; Siljander, Juhana; Urbano, José MiguelWe give a proof of the Hölder continuity of weak solutions of certain degenerate doubly nonlinear parabolic equations in measure spaces. We only assume the measure to be a doubling non-trivial Borel measure which supports a Poincaré inequality. The proof discriminates between large scales, for which a Harnack inequality is used, and small scales, that require intrinsic scaling methods.
On the well-posedness of a two-phase minimization problem
Urbano, José Miguel; Vorotnikov, DmitryWe prove a series of results concerning the emptiness and non-emptiness of a certain set of Sobolev functions related to the well-posedness of a two-phase minimization problem, involving both the p(x)-norm and the in nity norm. The results, although interesting in their own right, hold the promise of a wider applicability since they can be relevant in the context of other problems where minimization of the p-en...
Limits as p(x) of p(x)-harmonic functions
Manfredi, Juan J.; Rossi, Julio D.; Urbano, José MiguelIn this note we study the limit as p(x) ! 1of solutions to − p(x)u = 0 in a domain , with Dirichlet boundary conditions. Our approach consists in considering sequences of variable exponents converging uniformly to +1 and analyzing how the corresponding solutions of the problem converge and what equation is satisfied by the limit.
A mathematical model for a comprehensive approach to the dynamics of human colo...
Figueiredo, Isabel N.; Figueiredo, Pedro N.; Leal, Carlos; Urbano, José MiguelIn this paper, we propose mathematical models for the growth dynamics of aberrant crypt foci in the human colon, as well as for some of their characteristics, namely the apoptosis and proliferation indices. The models rely on logistic type differential equations and clinical observations at different times, and can arguably be used as an auxiliary screening tool for colon cancer. We report several results using...
The nonlinear N-membranes evolution problem
Rodrigues, José Francisco; Santos, Lisa; Urbano, José MiguelThe parabolic N-membranes problem for the p-Laplacian and the complete order constraint on the components of the solution is studied in what concerns the approximation, the regularity and the stability of the variational solutions. We extend to the evolutionary case the characterization of the Lagrange multipliers associated with the ordering constraint in terms of the characteristic functions of the coincidenc...
p(x)-Harmonic functions with unbounded exponent in a subdomain
Manfredi, Juan J.; Rossi, Julio D.; Urbano, José MiguelWe study the Dirichlet problem −div( ; ∇u ; p(x)−2∇u) = 0 in , with u = f on @ and p(x) = ∞ in D, a subdomain of the reference domain . The main issue is to give a proper sense to what a solution is. To this end, we consider the limit as n → ∞ of the solutions un to the corresponding problem when pn(x) = p(x)∧ n, in particular, with p = n in D. Under suitable assumptions on the data, we find that such a li...
Growth conditions and uniqueness of the Cauchy problem for the evolutionary inf...
Leonori, Tommaso; Urbano, José MiguelWe study the Cauchy problem for the parabolic infinity Laplace equation. We prove a new comparison principle and obtain uniqueness of viscosity solutions in the class of functions with a polinomial growth at infinity, improving previous results obtained assuming a linear growth.
On a doubly nonlinear diffusion model of chemotaxis with prevention of overcrow...
Bendahmane, Mostafa; Bürger, Raimund; Baier, Ricardo Ruiz; Urbano, José MiguelThis paper addresses the existence and regularity of weak solutions for a fully parabolic model of chemotaxis, with prevention of overcrowding, that degenerates in a two-sided fashion, including an extra nonlinearity represented by a p- Laplacian diffusion term. To prove the existence of weak solutions, a Schauder fixedpoint argument is applied to a regularized problem and the compactness method is used to pass...
New global a prior; estimates for the third-grade fluid equations
Steinhauer, Mark; Urbano, José Miguel; Videman, JuhaThis note bridges the gap between the existence and regularity classes for the third-grade Rivlin-Ericksen fluid equations. We obtain a new global a priori estimate, which conveys the precise regularity conditions that lead to the existence of a global in time regular solution. Copyright © 2006 John Wiley & Sons, Ltd. ; http://dx.doi.org/10.1002/mma.732
The obstacle problem for nonlinear elliptic equations with variable growth and ...
Rodrigues, José Francisco; Sanchón, Manel; Urbano, José MiguelThe aim of this paper is twofold: to prove, for L1-data, the existence and uniqueness of an entropy solution to the obstacle problem for nonlinear elliptic equations with variable growth, and to show some convergence and stability properties of the corresponding coincidence set. The latter follow from extending the Lewy–Stampacchia inequalities to the general framework of L1
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