Differential operators | Elliptic partial differential equations
In mathematics, the infinity Laplace (or -Laplace) operator is a 2nd-order partial differential operator, commonly abbreviated . It is alternately defined by or The 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 (generalized) 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. (Wikipedia).
Can You Define the Immeasurable?
What is infinity? Can you define something that, by definition, has no boundaries? A subject extensively studied by philosophers, mathematicians, and more recently, physicists and cosmologists, infinity still stands as an enigma of the intellectual world. We asked people from all walks of
From playlist Mathematics
What happens to limits at infinity. We also look at one of the uses of limits: continuity.
From playlist Life Science Math: Limits in calculus
A subject extensively studied by philosophers, mathematicians, and now recently, physicists, infinity is a uniquely universal enigma within the academic world. Thinkers clash over questions such as: Does infinity exist? What types of infinity are there? Watch the Full Program Here: https:
From playlist Mathematics
http://www.woodthatworks.com/kinetic-sculptures/infinity Infinity Kinetic sculpture by David C. Roy with actual sounds The video segments of the full sculpture have been endited to keep the total length of the video short. For a longer sequence https://youtu.be/nPUcQpyLBh0
From playlist Kinetic Sculpture
A classic calculus 1 limit problem, evaluating the limit of x-th root of x as x goes to infinity. This is an inf^0 indeterminate form example. We will have to convert the x-root of x to x^(1/x) and then write x as e^ln(x) and use L'Hopital's Rule. Try this next: what do you think what (inf
From playlist Calculus Limits
Definition of infinity In this video, I define the concept of infinity (as used in analysis), and explain what it means for sup(S) to be infinity. In particular, the least upper bound property becomes very elegant to write down. Check out my real numbers playlist: https://www.youtube.co
From playlist Real Numbers
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From playlist Calculus
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From playlist CALCULUS 1 CH 1 LIMITS & DERIVATIVES
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From playlist Summer School on PDE & Randomness
Calculus Limits at Infinity The Limit of 2/(4x + sin(x)) as x approaches infinity
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From playlist Calculus
Francesca Da Lio: Analysis of nonlocal conformal invariant variational problems, Lecture II
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From playlist Hausdorff School: Trending Tools
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From playlist Variational Methods in Geometry
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From playlist Yilin Wang - The Loewner Energy at the Crossroad of Random Conformal Geometry and Teichmueller Theory
Ancient solutions to geometric flows II - Panagiota Daskalopoulos
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From playlist Mathematics
Rafe Mazzeo - Minicourse - Lecture 1
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From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
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From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
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From playlist Mathematics
A PDE approach to scaling limit of random interface models on Z^d by Rajat Subhra Hazra
PROGRAM :UNIVERSALITY IN RANDOM STRUCTURES: INTERFACES, MATRICES, SANDPILES ORGANIZERS :Arvind Ayyer, Riddhipratim Basu and Manjunath Krishnapur DATE & TIME :14 January 2019 to 08 February 2019 VENUE :Madhava Lecture Hall, ICTS, Bangalore The primary focus of this program will be on the
From playlist Universality in random structures: Interfaces, Matrices, Sandpiles - 2019
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From playlist New Calculus Video Playlist