A Minimum Problem with Free Boundary for the p(x)−Laplace Operator

2011 ◽  
Vol 11 (1) ◽  
Author(s):  
A. Lyaghfouri
Keyword(s):  
Free Boundary ◽  
Lebesgue Measure ◽  
Laplace Operator ◽  
Lipschitz Continuity ◽  
Minimum Problem ◽  
Positive Density ◽  
Problem With Free Boundary

AbstractIn this paper we consider the problem of minimizing the functionalWe prove Lipschitz continuity for each minimizer u and establish the nondegeneracy at the free boundary (∂[u > 0]) ∩ Ω and the locally uniform positive density of the sets [u > 0] and [u = 0]. In particular we obtain that the Lebesgue measure of the free boundary is zero.

scholarly journals A minimum problem with free boundary in Orlicz spaces

2008 ◽  
Vol 218 (6) ◽  
pp. 1914-1971 ◽  
Author(s):  
Sandra Martínez ◽  
Noemi Wolanski
Keyword(s):  
Free Boundary ◽  
Orlicz Spaces ◽  
Minimum Problem ◽  
Problem With Free Boundary

The Two-dimensional Problem with Free Boundary in Problems of Medicine

2021 ◽  
Author(s):  
Fatimat Kh. Kudayeva ◽  
Aslan Kh. Zhemukhov ◽  
Aslan L. Nagorov ◽  
Arslan A. Kaygermazov ◽  
Diana A. Khashkhozheva ◽  
...  
Keyword(s):  
Free Boundary ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Problem With Free Boundary

Regularity results for solutions to the c-Plateau problem with free boundary having small singular set, and generally in codimension zero

2016 ◽  
Vol 9 (3) ◽  
pp. 259-282 ◽  
Author(s):  
Leobardo Rosales
Keyword(s):  
Free Boundary ◽  
Minimization Problem ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Plateau Problem ◽  
Singular Set ◽  
Codimension Two ◽  
Rectifiable Currents ◽  
Problem With Free Boundary ◽  
Regularity Results

AbstractWe prove two results for the c-Plateau problem, introduced in [17], which is a minimization problem for integer rectifiable currents. First, we prove there is no solution to the c-Plateau problem with free boundary having singular set of finite Hausdorff codimension two measure and with regular part having constant mean curvature. Second, we prove regularity up to Hausdorff codimension seven of the free boundary of top-dimensional solutions to the c-Plateau problem.

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