Elliptic partial differential equations
In mathematics, the p-Laplacian, or the p-Laplace operator, is a quasilinear elliptic partial differential operator of 2nd order. It is a nonlinear generalization of the Laplace operator, where is allowed to range over . It is written as Where the is defined as In the special case when , this operator reduces to the usual Laplacian. In general solutions of equations involving the p-Laplacian do not have second order derivatives in classical sense, thus solutions to these equations have to be understood as weak solutions. For example, we say that a function u belonging to the Sobolev space is a weak solution of if for every test function we have where denotes the standard scalar product. (Wikipedia).
Physics - Advanced E&M: Ch 1 Math Concepts (13 of 55) What is the Laplacian of a Scalar (Field)?
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Dong Zhang (7/27/22): Higher order eigenvalues for graph p-Laplacians
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From playlist Applied Geometry for Data Sciences 2022
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From playlist PARTIAL DIFFERENTIAL EQNS CH1 INTRODUCTION
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Juan Luis Vázquez: The theory of nonlinear diffusion with fractional operators
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From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
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