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- Infinity_Laplacian abstract "In mathematics, the infinity Laplace (or -Laplace) operator is a 2nd-order partial differential operator, commonly abbreviated . It is alternately defined byorThe first version avoids the singularity which occurs when the gradient vanishes, while the second version is homogeneous of order zero in the gradient. Verbally, the second version is the second derivative in the direction of the gradient. In the case of the infinity Laplace equation , the two definitions are equivalent.While the equation involves second derivatives, usually solutions are not twice differentiable, as evidenced by the well-known Aronsson solution . For this reason the correct notion of solutions is that given by the viscosity solutions.Viscosity solutions to the equation are also known as infinity harmonic functions. This terminology arises from the fact that the infinity Laplace operator first arose in the study of absolute minimizers for , and it can be viewed in a certain sense as the limit of the p-Laplacian as . More recently, viscosity solutions to the infinity Laplace equation have been identified with the payoff functions from randomized tug-of-war games. The game theory point of view has significantly improved the understanding of the partial differential equation itself.".
- Infinity_Laplacian wikiPageExternalLink BEJ.pdf.
- Infinity_Laplacian wikiPageID "32160914".
- Infinity_Laplacian wikiPageRevisionID "587854003".
- Infinity_Laplacian hasPhotoCollection Infinity_Laplacian.
- Infinity_Laplacian subject Category:Differential_operators.
- Infinity_Laplacian subject Category:Elliptic_partial_differential_equations.
- Infinity_Laplacian type Abstraction100002137.
- Infinity_Laplacian type Communication100033020.
- Infinity_Laplacian type DifferentialEquation106670521.
- Infinity_Laplacian type DifferentialOperators.
- Infinity_Laplacian type EllipticPartialDifferentialEquations.
- Infinity_Laplacian type Equation106669864.
- Infinity_Laplacian type Function113783816.
- Infinity_Laplacian type MathematicalRelation113783581.
- Infinity_Laplacian type MathematicalStatement106732169.
- Infinity_Laplacian type Message106598915.
- Infinity_Laplacian type Operator113786413.
- Infinity_Laplacian type PartialDifferentialEquation106670866.
- Infinity_Laplacian type Relation100031921.
- Infinity_Laplacian type Statement106722453.
- Infinity_Laplacian comment "In mathematics, the infinity Laplace (or -Laplace) operator is a 2nd-order partial differential operator, commonly abbreviated . It is alternately defined byorThe first version avoids the singularity which occurs when the gradient vanishes, while the second version is homogeneous of order zero in the gradient. Verbally, the second version is the second derivative in the direction of the gradient.".
- Infinity_Laplacian label "Infinity Laplacian".
- Infinity_Laplacian sameAs m.0gx1rrd.
- Infinity_Laplacian sameAs Q6030026.
- Infinity_Laplacian sameAs Q6030026.
- Infinity_Laplacian sameAs Infinity_Laplacian.
- Infinity_Laplacian wasDerivedFrom Infinity_Laplacian?oldid=587854003.
- Infinity_Laplacian isPrimaryTopicOf Infinity_Laplacian.