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In mathematics, the p-Laplacian, or the p- … 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.where denotes the standard scalar product.
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In mathematics, the p-Laplacian, or the p- … 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 if for every test function we have where denotes the standard scalar product.where denotes the standard scalar product.
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P-Laplacian
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