An inhomogeneous singular perturbation problem for the p(x)-Laplacian Dedicated to our dear friend and colleague Juan Luis Vázquez on the occasion of his 70th birthday
In this paper we study the following singular perturbation problem for the pϵ(x)-Laplacian: Δpϵ (x)uϵ:=div(|∇uϵ(x)|pϵ (x)-2∇ uϵ)=βϵ(uϵ)+fϵ,uϵ≥0, (Pϵ(fϵ, pϵ)) where ϵ>0, βϵ(s)=1/ϵβ(s/ϵ), with β a Lipschitz function satisfying β>0 in (0,1), β≡0 outside (0,1) and ∫β(s)ds=M. The functions...
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| Lenguaje: | Inglés |
| Publicado: |
Elsevier Ltd
2016
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| Acceso en línea: | Registro en Scopus DOI Handle Registro en la Biblioteca Digital |
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| LEADER | 08623caa a22008177a 4500 | ||
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| 001 | PAPER-15939 | ||
| 003 | AR-BaUEN | ||
| 005 | 20230518204647.0 | ||
| 008 | 190411s2016 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-84950248198 | |
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 030 | |a NOAND | ||
| 100 | 1 | |a Lederman, C. | |
| 245 | 1 | 3 | |a An inhomogeneous singular perturbation problem for the p(x)-Laplacian Dedicated to our dear friend and colleague Juan Luis Vázquez on the occasion of his 70th birthday |
| 260 | |b Elsevier Ltd |c 2016 | ||
| 270 | 1 | 0 | |m Wolanski, N.; IMAS-CONICET, Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos AiresArgentina; email: wolanski@dm.uba.ar |
| 506 | |2 openaire |e Política editorial | ||
| 504 | |a Aboulaich, R., Meskine, D., Souissi, A., New diffusion models in image processing (2008) Comput. Math. Appl., 56 (4), pp. 874-882 | ||
| 504 | |a Andersson, J., Weiss, G.S., A parabolic free boundary problem with Bernoulli type condition on the free boundary (2009) J. Reine Angew. Math., 627, pp. 213-235 | ||
| 504 | |a Berestycki, H., Caffarelli, L.A., Nirenberg, L., Uniform estimates for regularization of free boundary problems (1990) Analysis and Partial Differential Equations, 122, pp. 567-619. , Cora Sadosky, Lecture Notes in Pure and Applied Mathematics Marcel Dekker New York | ||
| 504 | |a Berestycki, H., Larrouturou, B., Quelques aspects mathématiques de la propagation des flammes prémélangées (1991) Nonlinear Partial Differential Equations and Their Applications, 10, pp. 65-129. , H. Brezis, J.L. Lions, Collège de France Seminar Pitman London | ||
| 504 | |a Caffarelli, L.A., Lederman, C., Wolanski, N., Uniform estimates and limits for a two phase parabolic singular perturbation problem (1997) Indiana Univ. Math. J., 46 (2), pp. 453-490 | ||
| 504 | |a Caffarelli, L.A., Lederman, C., Wolanski, N., Pointwise and viscosity solutions for the limit of a two phase parabolic singular perturbation problem (1997) Indiana Univ. Math. J., 46 (3), pp. 719-740 | ||
| 504 | |a Caffarelli, L.A., Vazquez, J.L., A free boundary problem for the heat equation arising in flame propagation (1995) Trans. Amer. Math. Soc., 347, pp. 411-441 | ||
| 504 | |a Challal, S., Lyaghfouri, A., Second order regularity for the p(x)-Laplace operator (2011) Math. Nachr., 284 (10), pp. 1270-1279 | ||
| 504 | |a Chen, Y., Levine, S., Rao, M., Variable exponent, linear growth functionals in image restoration (2006) SIAM J. Appl. Math., 66 (4), pp. 1383-1406 | ||
| 504 | |a Danielli, D., Petrosyan, A., Shahgholian, H., A singular perturbation problem for the p-Laplace operator (2003) Indiana Univ. Math. J., 52 (2), pp. 457-476 | ||
| 504 | |a Diening, L., Harjulehto, P., Hasto, P., Ruzicka, M., (2011) Lebesque and Sobolev Spaces with Variable Exponents, 2017. , Lecture Notes in Mathematics Springer | ||
| 504 | |a Fan, X., Global C1,α regularity for variable exponent elliptic equations in divergence form (2007) J. Differential Equations, 235, pp. 397-417 | ||
| 504 | |a Fernandez Bonder, J., Martínez, S., Wolanski, N., A free boundary problem for the p(x)-Laplacian (2010) Nonlinear Anal., 72, pp. 1078-1103 | ||
| 504 | |a Kováčik, O., Rákosník, J., On spaces Lp(x) and Wk,p(x) (1991) Czechoslovak Math. J., 41, pp. 592-618 | ||
| 504 | |a Lederman, C., Oelz, D., A quasilinear parabolic singular perturbation problem (2008) Interfaces Free Bound., 10 (4), pp. 447-482 | ||
| 504 | |a Lederman, C., Wolanski, N., Viscosity solutions and regularity of the free boundary for the limit of an elliptic two phase singular perturbation problem (1998) Ann. Sc. Norm. Super. Pisa Cl. Sci. (4), 27 (2), pp. 253-288 | ||
| 504 | |a Lederman, C., Wolanski, N., A two phase elliptic singular perturbation problem with a forcing term (2006) J. Math. Pures Appl., 86 (6), pp. 552-589 | ||
| 504 | |a Lederman, C., Wolanski, N., Singular perturbation in a nonlocal diffusion problem (2006) Comm. Partial Differential Equations, 31 (2), pp. 195-241 | ||
| 504 | |a Lederman, C., Wolanski, N., Weak Solutions and Regularity of the Interface in An Inhomogeneous Free Boundary Problem for the P(x)-Laplacian, , submitted | ||
| 504 | |a Lederman, C., Wolanski, N., On Inhomogeneous Minimization Problems for the P(x)-Laplacian, , in preparation | ||
| 504 | |a Martínez, S., Wolanski, N., A singular perturbation problem for a quasi-linear operator satisfying the natural growth condition of Lieberman (2009) SIAM J. Math. Anal., 40 (1), pp. 318-359 | ||
| 504 | |a Moreira, D., Wang, L., Singular perturbation method for inhomogeneous nonlinear free boundary problems (2014) Calc. Var. Partial Differential Equations, 49 (3-4), pp. 1237-1261 | ||
| 504 | |a Ricarte, G., Teixeira, E., Fully nonlinear singularly perturbed equations and asymptotic free boundaries (2011) J. Funct. Anal., 261, pp. 1624-1673 | ||
| 504 | |a Ruzicka, M., (2000) Electrorheological Fluids: Modeling and Mathematical Theory, , Springer-Verlag Berlin | ||
| 504 | |a Tolksdorf, P., Regularity for a more general class of quasilinear elliptic equations (1984) J. Differential Equations, 51, pp. 126-150 | ||
| 504 | |a Vazquez, J.L., The free boundary problem for the heat equation with fixed gradient condition (1996) Free Boundary Problems, Theory and Applications (Zakopane, 1995), 363, pp. 277-302. , M. Niezgódka, P. Strzelecki, Pitman Res. Notes Math. Ser. Longman Harlow | ||
| 504 | |a Weiss, G.S., A singular limit arising in combustion theory: Fine properties of the free boundary (2003) Calc. Var. Partial Differential Equations, 17 (3), pp. 311-340 | ||
| 504 | |a Wolanski, N., Local bounds, Harnack inequality and Hölder continuity for divergence type elliptic equations with non-standard growth (2015) Rev. Un. Mat. Argentina, 56 (1), pp. 73-105 | ||
| 504 | |a Zeldovich, Ya.B., Frank-Kamenetski, D.A., The theory of thermal propagation of flames (1938) Zh. Fiz. Khim., 12, pp. 100-105. , (in Russian); English translation in "Collected Works of Ya. B. Zeldovich", vol. 1, Princeton Univ. Press, 1992 | ||
| 520 | 3 | |a In this paper we study the following singular perturbation problem for the pϵ(x)-Laplacian: Δpϵ (x)uϵ:=div(|∇uϵ(x)|pϵ (x)-2∇ uϵ)=βϵ(uϵ)+fϵ,uϵ≥0, (Pϵ(fϵ, pϵ)) where ϵ>0, βϵ(s)=1/ϵβ(s/ϵ), with β a Lipschitz function satisfying β>0 in (0,1), β≡0 outside (0,1) and ∫β(s)ds=M. The functions uϵ, fϵ and pϵ are uniformly bounded. We prove uniform Lipschitz regularity, we pass to the limit (ϵ→0) and we show that, under suitable assumptions, limit functions are weak solutions to the free boundary problem: u≥0 and {Δp(x)u = f in {u>0}u=0,|∇u|=λ ∗(x)on ∂{u>0} (P(f, p, λ∗)) with λ∗ (x)=(p(x)/p(x)-1 M)1/p(x), p = lim pϵ and f = lim fϵ. In Lederman and Wolanski (submitted) we prove that the free boundary of a weak solution is a C1,α surface near flat free boundary points. This result applies, in particular, to the limit functions studied in this paper. © 2015 Elsevier Ltd. All rights reserved. |l eng | |
| 593 | |a IMAS-CONICET, Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, (1428), Argentina | ||
| 690 | 1 | 0 | |a FREE BOUNDARY PROBLEM |
| 690 | 1 | 0 | |a SINGULAR PERTURBATION |
| 690 | 1 | 0 | |a VARIABLE EXPONENT SPACES |
| 690 | 1 | 0 | |a BOUNDARY VALUE PROBLEMS |
| 690 | 1 | 0 | |a FREE-BOUNDARY PROBLEMS |
| 690 | 1 | 0 | |a LIPSCHITZ FUNCTIONS |
| 690 | 1 | 0 | |a LIPSCHITZ REGULARITY |
| 690 | 1 | 0 | |a P (X)-LAPLACIAN |
| 690 | 1 | 0 | |a SINGULAR PERTURBATION PROBLEMS |
| 690 | 1 | 0 | |a SINGULAR PERTURBATIONS |
| 690 | 1 | 0 | |a UNIFORMLY BOUNDED |
| 690 | 1 | 0 | |a VARIABLE EXPONENTS |
| 690 | 1 | 0 | |a LAPLACE TRANSFORMS |
| 700 | 1 | |a Wolanski, N. | |
| 773 | 0 | |d Elsevier Ltd, 2016 |g v. 138 |h pp. 300-325 |p Nonlinear Anal Theory Methods Appl |x 0362546X |w (AR-BaUEN)CENRE-254 |t Nonlinear Analysis, Theory, Methods and Applications | |
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| 856 | 4 | 0 | |u https://doi.org/10.1016/j.na.2015.09.026 |y DOI |
| 856 | 4 | 0 | |u https://hdl.handle.net/20.500.12110/paper_0362546X_v138_n_p300_Lederman |y Handle |
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