2012/04/30 by Maria del Mar Gonzalez, María del Mar González, Maria Gualdani +5
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Applied mathematics #Bernoulli's principle #Boundary (topology) #Boundary value problem #FOS: Mathematics #Free boundary problem #Geometric Analysis and Curvature Flows #Geometry #Mathematical analysis #Mathematical optimization #Mathematics #Nonlinear Partial Differential Equations #Operator (biology) #Physics #Regular polygon #Simplicity #math.AP
paper · pdf · doi:10.48550/arxiv.1204.6578
published in arXiv (Cornell University) (Cornell University)
arxiv created 2012/04/30 · openalex publication_date 2012/04/30 · arxiv updated 2012/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider a free boundary problem for the p-Laplace operator which is related to the so-called Bernoulli free boundary problem. In this formulation, the classical boundary gradient condition is replaced by a condition on the distance between two different level surfaces of the solution. For suitable scalings our model converges to the classical Bernoulli problem; one of the advantages in this new formulation lies in the simplicity of the arguments, since one does not need to consider the boundary gradient. We shall study this problem in convex and other regimes, and establish existence and qualitative theory.