Add to ORKGAbstract. We study the existence of a set with minimal perime-ter that separates two disjoint sets in a metric measure space equipped with a doubling measure and supporting a Poincare ́ in-equality. A measure constructed by De Giorgi is used to state a relaxed problem, whose solution coincides with the solution to the original problem for measure theoretically thick sets. Moreover, we study properties of the De Giorgi measure on metric measure spaces and show that it is comparable to the Hausdorff measure of codimension one. We also explore the relationship between the De Giorgi measure and the variational capacity of order one. The theory of functions of bounded variation on metric spaces is used extensively in the arguments. 1
This dissertation studies existence and regularity properties of functions related to the calculus o...
In this paper we study problems related to parabolic partial differential equations in metric measur...
We study the geometry of domains in complete metric measure spaces equipped with a doubling measure ...
Abstract. We study the existence of a set with minimal perime-ter that separates two disjoint sets i...
We study the existence of a set with minimal perimeter that separates two disjoint sets in a metric ...
W.K. ALLARD: On the first variation of area and generalized mean curvature.- F.J. ALMGREN Jr.: Geome...
This master thesis aims to study some of the work of the Italian mathematician Ennio De Giorgi which...
The main result of this dissertation is the provision of conditions, weaker than those of Cheeger [C...
The Plateau problem consists of nding the set that minimizes its perimeter among all sets of a cer...
We consider two notions of functions of bounded variation in complete metric measure spaces, one due...
This paper studies analytic aspects of so-called resistance conditions on metric measure spaces with...
We study a measure-theoretic notion of connectedness for sets of finite perimeter in the setting of ...
We study two notions of Dirichlet problem associated with BV energy minimizers (also called function...
Abstract. This paper studies regularity of perimiter quasimin-imizing sets in metric measure spaces ...
Publisher Copyright: © 2022 The Author(s)We discuss a purely variational approach to the total varia...
This dissertation studies existence and regularity properties of functions related to the calculus o...
In this paper we study problems related to parabolic partial differential equations in metric measur...
We study the geometry of domains in complete metric measure spaces equipped with a doubling measure ...
Abstract. We study the existence of a set with minimal perime-ter that separates two disjoint sets i...
We study the existence of a set with minimal perimeter that separates two disjoint sets in a metric ...
W.K. ALLARD: On the first variation of area and generalized mean curvature.- F.J. ALMGREN Jr.: Geome...
This master thesis aims to study some of the work of the Italian mathematician Ennio De Giorgi which...
The main result of this dissertation is the provision of conditions, weaker than those of Cheeger [C...
The Plateau problem consists of nding the set that minimizes its perimeter among all sets of a cer...
We consider two notions of functions of bounded variation in complete metric measure spaces, one due...
This paper studies analytic aspects of so-called resistance conditions on metric measure spaces with...
We study a measure-theoretic notion of connectedness for sets of finite perimeter in the setting of ...
We study two notions of Dirichlet problem associated with BV energy minimizers (also called function...
Abstract. This paper studies regularity of perimiter quasimin-imizing sets in metric measure spaces ...
Publisher Copyright: © 2022 The Author(s)We discuss a purely variational approach to the total varia...
This dissertation studies existence and regularity properties of functions related to the calculus o...
In this paper we study problems related to parabolic partial differential equations in metric measur...
We study the geometry of domains in complete metric measure spaces equipped with a doubling measure ...