On a penalization method for an evolutionary free boundary problem with volume constraint

0448814 - MÚ 2016 RIV JP eng J - Journal Article
Muhammad, R. Z. - Švadlenka, Karel
On a penalization method for an evolutionary free boundary problem with volume constraint.
Advances in Mathematical Sciences and Applications. Roč. 24, č. 1 (2014), s. 85-101. ISSN 1343-4373
Institutional support: RVO:67985840
Keywords : penalization method * boundary problem
Subject RIV: BA - General Mathematics

We consider the problem of successively minimizing the functional ... over all nonnegative functions ... whose set of positive values have Lebesgue measure equal to ... for a given nonnegative Lipschitz continuous function ... We use an approximation method that penalizes only the increase in measure of the set ... We prove the existence and regularity of the minimizer and investigate its behavior for sufficiently large penalty parameter. Without relying on the smoothness of the free boundary, we show that the measure of the set ... adjusts to its prescribed value provided is large enough; hence, the solution to the original problem is attained without having to take to infinity. To end, we show the existence of a minimizing movement and some of its properties.
Permanent Link: http://hdl.handle.net/11104/0250418