A local monotonicity formula for an inhomogenous singular perturbation problem and applications

In this paper we prove a local monotonicity formula for solutions to an inhomogeneous singularly perturbed diffusion problem of interest in combustion. This type of monotonicity formula has proved to be very useful for the study of the regularity of limits u of solutions of the singular perturbation...

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Autores principales:	Lederman, C., Wolanski, N.
Formato:	JOUR
Materias:	Combustion Inhomogeneous problems Monotonicity formula Singular perturbation problems
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_03733114_v187_n2_p197_Lederman
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

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spelling	todo:paper_03733114_v187_n2_p197_Lederman2023-10-03T15:30:16Z A local monotonicity formula for an inhomogenous singular perturbation problem and applications Lederman, C. Wolanski, N. Combustion Inhomogeneous problems Monotonicity formula Singular perturbation problems In this paper we prove a local monotonicity formula for solutions to an inhomogeneous singularly perturbed diffusion problem of interest in combustion. This type of monotonicity formula has proved to be very useful for the study of the regularity of limits u of solutions of the singular perturbation problem and of {u > 0}, in the global homogeneous case. As a consequence of this formula we prove that u has an asymptotic development at every point in {u > 0} where there is a nonhorizontal tangent ball. These kind of developments have been essential for the proof of the regularity of {u > 0} for Bernoulli and Stefan free boundary problems. We also present applications of our results to the study of the regularity of {u > 0} in the stationary case including, in particular, its regularity in the case of energy minimizers. We present as well a regularity result for traveling waves of a combustion model that relies on our monotonicity formula and its consequences.The fact that our results hold for the inhomogeneous problem allows a very wide applicability. Indeed, they may be applied to problems with nonlocal diffusion and/or transport. © 2007 Springer-Verlag. Fil:Lederman, C. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Wolanski, N. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_03733114_v187_n2_p197_Lederman
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Combustion Inhomogeneous problems Monotonicity formula Singular perturbation problems
spellingShingle	Combustion Inhomogeneous problems Monotonicity formula Singular perturbation problems Lederman, C. Wolanski, N. A local monotonicity formula for an inhomogenous singular perturbation problem and applications
topic_facet	Combustion Inhomogeneous problems Monotonicity formula Singular perturbation problems
description	In this paper we prove a local monotonicity formula for solutions to an inhomogeneous singularly perturbed diffusion problem of interest in combustion. This type of monotonicity formula has proved to be very useful for the study of the regularity of limits u of solutions of the singular perturbation problem and of {u > 0}, in the global homogeneous case. As a consequence of this formula we prove that u has an asymptotic development at every point in {u > 0} where there is a nonhorizontal tangent ball. These kind of developments have been essential for the proof of the regularity of {u > 0} for Bernoulli and Stefan free boundary problems. We also present applications of our results to the study of the regularity of {u > 0} in the stationary case including, in particular, its regularity in the case of energy minimizers. We present as well a regularity result for traveling waves of a combustion model that relies on our monotonicity formula and its consequences.The fact that our results hold for the inhomogeneous problem allows a very wide applicability. Indeed, they may be applied to problems with nonlocal diffusion and/or transport. © 2007 Springer-Verlag.
format	JOUR
author	Lederman, C. Wolanski, N.
author_facet	Lederman, C. Wolanski, N.
author_sort	Lederman, C.
title	A local monotonicity formula for an inhomogenous singular perturbation problem and applications
title_short	A local monotonicity formula for an inhomogenous singular perturbation problem and applications
title_full	A local monotonicity formula for an inhomogenous singular perturbation problem and applications
title_fullStr	A local monotonicity formula for an inhomogenous singular perturbation problem and applications
title_full_unstemmed	A local monotonicity formula for an inhomogenous singular perturbation problem and applications
title_sort	local monotonicity formula for an inhomogenous singular perturbation problem and applications
url	http://hdl.handle.net/20.500.12110/paper_03733114_v187_n2_p197_Lederman
work_keys_str_mv	AT ledermanc alocalmonotonicityformulaforaninhomogenoussingularperturbationproblemandapplications AT wolanskin alocalmonotonicityformulaforaninhomogenoussingularperturbationproblemandapplications AT ledermanc localmonotonicityformulaforaninhomogenoussingularperturbationproblemandapplications AT wolanskin localmonotonicityformulaforaninhomogenoussingularperturbationproblemandapplications
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A local monotonicity formula for an inhomogenous singular perturbation problem and applications

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