A local monotonicity formula for an inhomogeneous singular perturbation problem and applications: Part II
In this paper we continue with our work in Lederman and Wolanski (Ann Math Pura Appl 187(2):197-220, 2008) where we developed a local monotonicity formula for solutions to an inhomogeneous singular perturbation problem of interest in combustion theory. There we proved local monotonicity formulae for...
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2010
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| 008 | 190411s2010 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-70449529891 | |
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| 100 | 1 | |a Lederman, C. | |
| 245 | 1 | 2 | |a A local monotonicity formula for an inhomogeneous singular perturbation problem and applications: Part II |
| 260 | |c 2010 | ||
| 270 | 1 | 0 | |m Lederman, C.; Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina; email: clederma@dm.uba.ar |
| 506 | |2 openaire |e Política editorial | ||
| 504 | |a Berestycki, H., Caffarelli, L.A., Nirenberg, L., Uniform estimates for regularization of free boundary problems (1990) Analysis and Partial Differential Equations. Lecture Notes in Pure and Applied Mathematics, 122, pp. 567-619. , In: Sadosky, C. (ed.), Marcel Dekker, New York | ||
| 504 | |a Buckmaster, J.D., Ludford, G.S.S., (1982) Theory of Laminar Flames, , Cambridge: Cambridge University Press | ||
| 504 | |a Caffarelli, L.A., A Harnack inequality approach to the regularity of free boundaries. Part II: Flat free boundaries are Lipschitz (1989) Comm. Pure Appl. Math., 42, pp. 55-78 | ||
| 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 Evans, L., Gariepy, R., (1992) Measure Theory and Fine Properties of Functions. Studies in Advanced Mathematics, , Boca Raton: CRC Press | ||
| 504 | |a Lederman, C., Wolanski, N., Singular perturbation in a nonlocal diffusion model (2006) Commun. PDE, 31 (2), pp. 195-241 | ||
| 504 | |a Lederman, C., Wolanski, N., A local monotonicity formula for an inhomogeneous singular perturbation problem and applications (2008) Ann. Math. Pura Appl., 187 (2), pp. 197-220 | ||
| 504 | |a Lederman, C., Wolanski, N., A two phase elliptic singular perturbation problem with a forcing term (2006) J. Math. Pures Appl., 86, pp. 552-589 | ||
| 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), Pitman Res. Notes Math. Ser., 363, pp. 277-302. , In: Niezgódka, M., Strzelecki, P. (eds.), Longman, Harlow | ||
| 504 | |a Weiss, G.S., A singular limit arising in combustion theory: Fine properties of the free boundary (2003) Calc. Var. Partial Differ. Equ., 17 (3), pp. 311-340 | ||
| 520 | 3 | |a In this paper we continue with our work in Lederman and Wolanski (Ann Math Pura Appl 187(2):197-220, 2008) where we developed a local monotonicity formula for solutions to an inhomogeneous singular perturbation problem of interest in combustion theory. There we proved local monotonicity formulae for solutions u<sup/> to the singular perturbation problem and for u = lim u<sup/>, assuming that both and u<sup/> and u were defined in an arbitrary domain D in ℝN+1. In the present work we obtain global monotonicity formulae for limit functions u that are globally defined, while u<sup/> are not. We derive such global formulae from a local one that we prove here. In particular, we obtain a global monotonicity formula for blow up limits u0 of limit functions u that are not globally defined. As a consequence of this formula, we characterize blow up limits u0 in terms of the value of a density at the blow up point. We also present applications of the results in this paper to the study of the regularity of ∂{u > 0} (the flame front in combustion models). The fact that our results hold for the inhomogeneous singular perturbation problem allows a very wide applicability, for instance to problems with nonlocal diffusion and/or transport. © Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag 2009. |l eng | |
| 593 | |a Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina | ||
| 650 | 1 | 7 | |2 spines |a COMBUSTION |
| 690 | 1 | 0 | |a INHOMOGENEOUS PROBLEMS |
| 690 | 1 | 0 | |a MONOTONICITY FORMULA |
| 690 | 1 | 0 | |a SINGULAR PERTURBATION PROBLEMS |
| 700 | 1 | |a Wolanski, N. | |
| 773 | 0 | |d 2010 |g v. 189 |h pp. 25-46 |k n. 1 |p Ann. Mat. Pura Appl. |x 03733114 |w (AR-BaUEN)CENRE-1530 |t Annali di Matematica Pura ed Applicata | |
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| 856 | 4 | 0 | |u https://doi.org/10.1007/s10231-009-0099-4 |y DOI |
| 856 | 4 | 0 | |u https://hdl.handle.net/20.500.12110/paper_03733114_v189_n1_p25_Lederman |y Handle |
| 856 | 4 | 0 | |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03733114_v189_n1_p25_Lederman |y Registro en la Biblioteca Digital |
| 961 | |a paper_03733114_v189_n1_p25_Lederman |b paper |c PE | ||
| 962 | |a info:eu-repo/semantics/article |a info:ar-repo/semantics/artículo |b info:eu-repo/semantics/publishedVersion | ||
| 999 | |c 69147 | ||