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Tatiana Toro  Geometry of measures and applications (Part 5)
/ Fanny Bastien
/ 19062015
/ Canalu.fr
Toro Tatiana
Voir le résumé
Voir le résumé
In the 1920's Besicovitch studied
linearly measurable sets in the plane, that is sets with locally finite
"length". The basic question he addressed was whether the infinitesimal
properties of the "length" of a set E in the plane yield geometric
information on E itself. This simple question marks the beginning of the
study of the geometry of measures and the associated field known as
Geometric Measure Theory (GMT).
In
this series of lectures we will present some of the main results in the
area concerning the regularity of the support of a measure in terms of
the behavior of its density or in terms of its tangent structure. We
will discuss applications to PDEs, free boundary regularity problem and
harmonic analysis. The aim is that the GMT component of the minicourse
will be self contained. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, geometric measure theory, calculus of variation

Accéder à la ressource


Tatiana Toro  Geometry of measures and applications (Part 4)
/ Fanny Bastien
/ 18062015
/ Canalu.fr
Toro Tatiana
Voir le résumé
Voir le résumé
In the 1920's Besicovitch studied
linearly measurable sets in the plane, that is sets with locally finite
"length". The basic question he addressed was whether the infinitesimal
properties of the "length" of a set E in the plane yield geometric
information on E itself. This simple question marks the beginning of the
study of the geometry of measures and the associated field known as
Geometric Measure Theory (GMT).
In
this series of lectures we will present some of the main results in the
area concerning the regularity of the support of a measure in terms of
the behavior of its density or in terms of its tangent structure. We
will discuss applications to PDEs, free boundary regularity problem and
harmonic analysis. The aim is that the GMT component of the minicourse
will be self contained. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, geometric measure theory, calculus of variation

Accéder à la ressource


Tatiana Toro  Geometry of measures and applications (Part 3)
/ Fanny Bastien
/ 17062015
/ Canalu.fr
Toro Tatiana
Voir le résumé
Voir le résumé
In the 1920's Besicovitch studied
linearly measurable sets in the plane, that is sets with locally finite
"length". The basic question he addressed was whether the infinitesimal
properties of the "length" of a set E in the plane yield geometric
information on E itself. This simple question marks the beginning of the
study of the geometry of measures and the associated field known as
Geometric Measure Theory (GMT).
In
this series of lectures we will present some of the main results in the
area concerning the regularity of the support of a measure in terms of
the behavior of its density or in terms of its tangent structure. We
will discuss applications to PDEs, free boundary regularity problem and
harmonic analysis. The aim is that the GMT component of the minicourse
will be self contained. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, geometric measure theory, calculus of variation

Accéder à la ressource


Tatiana Toro  Geometry of measures and applications (Part 2)
/ Fanny Bastien
/ 16062015
/ Canalu.fr
Toro Tatiana
Voir le résumé
Voir le résumé
In the 1920's Besicovitch studied
linearly measurable sets in the plane, that is sets with locally finite
"length". The basic question he addressed was whether the infinitesimal
properties of the "length" of a set E in the plane yield geometric
information on E itself. This simple question marks the beginning of the
study of the geometry of measures and the associated field known as
Geometric Measure Theory (GMT).
In
this series of lectures we will present some of the main results in the
area concerning the regularity of the support of a measure in terms of
the behavior of its density or in terms of its tangent structure. We
will discuss applications to PDEs, free boundary regularity problem and
harmonic analysis. The aim is that the GMT component of the minicourse
will be self contained. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, geometric measure theory, calculus of variation

Accéder à la ressource


Tatiana Toro  Geometry of measures and applications (Part 1)
/ Fanny Bastien
/ 16062015
/ Canalu.fr
Toro Tatiana
Voir le résumé
Voir le résumé
In the 1920's Besicovitch studied
linearly measurable sets in the plane, that is sets with locally finite
"length". The basic question he addressed was whether the infinitesimal
properties of the "length" of a set E in the plane yield geometric
information on E itself. This simple question marks the beginning of the
study of the geometry of measures and the associated field known as
Geometric Measure Theory (GMT).
In
this series of lectures we will present some of the main results in the
area concerning the regularity of the support of a measure in terms of
the behavior of its density or in terms of its tangent structure. We
will discuss applications to PDEs, free boundary regularity problem and
harmonic analysis. The aim is that the GMT component of the minicourse
will be self contained. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, geometric measure theory, calculus of variation

Accéder à la ressource


Yoshihiro Tonegawa  Analysis on the mean curvature flow and the reactiondiffusion approximation (Part 5)
/ Fanny Bastien
/ 18062015
/ Canalu.fr
Tonegawa Yoshihiro
Voir le résumé
Voir le résumé
The course covers two separate
but closely related topics. The first topic is the mean curvature flow
in the framework of GMT due to Brakke. It is a flow of varifold moving
by the generalized mean curvature. Starting from a quick review on the
necessary tools and facts from GMT and the definition of the Brakke mean
curvature flow, I will give an overview on the proof of the local
regularity theorem. The second topic is the reactiondiffusion
approximation of phase boundaries with key words such as the
ModicaMortola functional and the AllenCahn equation. Their singular
perturbation problems are related to objects such as minimal surfaces
and mean curvature flows in the framework of GMT. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, geometric measure theory, calculus of variation

Accéder à la ressource


Yoshihiro Tonegawa  Analysis on the mean curvature flow and the reactiondiffusion approximation (Part 4)
/ Fanny Bastien
/ 17062015
/ Canalu.fr
Tonegawa Yoshihiro
Voir le résumé
Voir le résumé
The course covers two separate
but closely related topics. The first topic is the mean curvature flow
in the framework of GMT due to Brakke. It is a flow of varifold moving
by the generalized mean curvature. Starting from a quick review on the
necessary tools and facts from GMT and the definition of the Brakke mean
curvature flow, I will give an overview on the proof of the local
regularity theorem. The second topic is the reactiondiffusion
approximation of phase boundaries with key words such as the
ModicaMortola functional and the AllenCahn equation. Their singular
perturbation problems are related to objects such as minimal surfaces
and mean curvature flows in the framework of GMT. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, geometric measure theory, calculus of variation

Accéder à la ressource


Yoshihiro Tonegawa  Analysis on the mean curvature flow and the reactiondiffusion approximation (Part 3)
/ Fanny Bastien
/ 17062015
/ Canalu.fr
Tonegawa Yoshihiro
Voir le résumé
Voir le résumé
The course covers two separate
but closely related topics. The first topic is the mean curvature flow
in the framework of GMT due to Brakke. It is a flow of varifold moving
by the generalized mean curvature. Starting from a quick review on the
necessary tools and facts from GMT and the definition of the Brakke mean
curvature flow, I will give an overview on the proof of the local
regularity theorem. The second topic is the reactiondiffusion
approximation of phase boundaries with key words such as the
ModicaMortola functional and the AllenCahn equation. Their singular
perturbation problems are related to objects such as minimal surfaces
and mean curvature flows in the framework of GMT. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, geometric measure theory, calculus of variation

Accéder à la ressource


Yoshihiro Tonegawa  Analysis on the mean curvature flow and the reactiondiffusion approximation (Part 2)
/ Fanny Bastien
/ 16062015
/ Canalu.fr
Tonegawa Yoshihiro
Voir le résumé
Voir le résumé
The course covers two separate
but closely related topics. The first topic is the mean curvature flow
in the framework of GMT due to Brakke. It is a flow of varifold moving
by the generalized mean curvature. Starting from a quick review on the
necessary tools and facts from GMT and the definition of the Brakke mean
curvature flow, I will give an overview on the proof of the local
regularity theorem. The second topic is the reactiondiffusion
approximation of phase boundaries with key words such as the
ModicaMortola functional and the AllenCahn equation. Their singular
perturbation problems are related to objects such as minimal surfaces
and mean curvature flows in the framework of GMT. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, geometric measure theory, calculus of variation

Accéder à la ressource


Yoshihiro Tonegawa  Analysis on the mean curvature flow and the reactiondiffusion approximation (Part 1)
/ Fanny Bastien
/ 15062015
/ Canalu.fr
Tonegawa Yoshihiro
Voir le résumé
Voir le résumé
The course covers two separate
but closely related topics. The first topic is the mean curvature flow
in the framework of GMT due to Brakke. It is a flow of varifold moving
by the generalized mean curvature. Starting from a quick review on the
necessary tools and facts from GMT and the definition of the Brakke mean
curvature flow, I will give an overview on the proof of the local
regularity theorem. The second topic is the reactiondiffusion
approximation of phase boundaries with key words such as the
ModicaMortola functional and the AllenCahn equation. Their singular
perturbation problems are related to objects such as minimal surfaces
and mean curvature flows in the framework of GMT. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, geometric measure theory, calculus of variation

Accéder à la ressource


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