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- Obstacle_problem abstract "The obstacle problem is a classic motivating example in the mathematical study of variational inequalities and free boundary problems. The problem is to find the equilibrium position of an elastic membrane whose boundary is held fixed, and which is constrained to lie above a given obstacle. It is deeply related to the study of minimal surfaces and the capacity of a set in potential theory as well. Applications include the study of fluid filtration in porous media, constrained heating, elasto-plasticity, optimal control, and financial mathematics.The mathematical formulation of the problem is to seek minimizers of the Dirichlet energy functional, in some domain where the functions represent the vertical displacement of the membrane. In addition to satisfying Dirichlet boundary conditions corresponding to the fixed boundary of the membrane, the functions are in addition constrained to be greater than some given obstacle function . The solution breaks down into a region where the solution is equal to the obstacle function, known as the contact set, and a region where the solution is above the obstacle. The interface between the two regions is the free boundary.In general, the solution is continuous and possesses Lipschitz continuous first derivatives, but that the solution is generally discontinuous in the second derivatives across the free boundary. The free boundary is characterized as a Hölder continuous surface except at certain singular points, which reside on a smooth manifold.".
- Obstacle_problem wikiPageExternalLink SDE.course.pdf.
- Obstacle_problem wikiPageExternalLink volume.php?lg=e&rid=32847.
- Obstacle_problem wikiPageExternalLink obstacle-long.pdf.
- Obstacle_problem wikiPageExternalLink u2105854886n6282.
- Obstacle_problem wikiPageID "19487617".
- Obstacle_problem wikiPageRevisionID "599230325".
- Obstacle_problem hasPhotoCollection Obstacle_problem.
- Obstacle_problem sign Alessandro_Faedo.
- Obstacle_problem text "Qualche tempo dopo Stampacchia, partendo sempre dalla sua disequazione variazionale, aperse un nuovo campo di ricerche che si rivelò importante e fecondo. Si tratta di quello che oggi è chiamato il problema dell'ostacolo.".
- Obstacle_problem subject Category:Calculus_of_variations.
- Obstacle_problem subject Category:Partial_differential_equations.
- Obstacle_problem type Abstraction100002137.
- Obstacle_problem type Communication100033020.
- Obstacle_problem type DifferentialEquation106670521.
- Obstacle_problem type Equation106669864.
- Obstacle_problem type MathematicalStatement106732169.
- Obstacle_problem type Message106598915.
- Obstacle_problem type PartialDifferentialEquation106670866.
- Obstacle_problem type PartialDifferentialEquations.
- Obstacle_problem type Statement106722453.
- Obstacle_problem comment "The obstacle problem is a classic motivating example in the mathematical study of variational inequalities and free boundary problems. The problem is to find the equilibrium position of an elastic membrane whose boundary is held fixed, and which is constrained to lie above a given obstacle. It is deeply related to the study of minimal surfaces and the capacity of a set in potential theory as well.".
- Obstacle_problem label "Obstacle problem".
- Obstacle_problem label "Problème de l'obstacle".
- Obstacle_problem sameAs Problème_de_l'obstacle.
- Obstacle_problem sameAs m.04mx4tj.
- Obstacle_problem sameAs Q3406250.
- Obstacle_problem sameAs Q3406250.
- Obstacle_problem sameAs Obstacle_problem.
- Obstacle_problem wasDerivedFrom Obstacle_problem?oldid=599230325.
- Obstacle_problem isPrimaryTopicOf Obstacle_problem.