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A calculus for a class of finitely degenerate pseudodifferential operators

Ingo Witt (2003)

Banach Center Publications

For a class of degenerate pseudodifferential operators, local parametrices are constructed. This is done in the framework of a pseudodifferential calculus upon adding conditions of trace and potential type, respectively, along the boundary on which the operators degenerate.

A nonlinear eigenvalue problem with indefinite weights related to the Sobolev trace embedding.

Julián Fernández Bonder, Julio D. Rossi (2002)

Publicacions Matemàtiques

In this paper we study the Sobolev trace embedding W1,p(Ω) → LpV (∂Ω), where V is an indefinite weight. This embedding leads to a nonlinear eigenvalue problem where the eigenvalue appears at the (nonlinear) boundary condition. We prove that there exists a sequence of variational eigenvalues λk / +∞ and then show that the first eigenvalue is isolated, simple and monotone with respect to the weight. Then we prove a nonexistence result related to the first eigenvalue and we end this article with the...

A note on a critical problem with natural growth in the gradient

Boumediene Abdellaoui, Ireneo Peral (2006)

Journal of the European Mathematical Society

The paper analyzes the influence on the meaning of natural growth in the gradient of a perturbation by a Hardy potential in some elliptic equations. Indeed, in the case of the Laplacian the natural problem becomes Δ u Λ N u | x | 2 = u + N 2 2 u | x | 2 x 2 | x | ( N 2 ) / 2 + λ f ( x ) in Ω , u = 0 on Ω , Λ N = ( ( N 2 ) / 2 ) 2 . This problem is a particular case of problem (2). Notice that ( N 2 ) / 2 is optimal as coefficient and exponent on the right hand side.

A refinement of the radial Pohozaev identity

Florin Catrina (2010)

Mathematica Bohemica

In this article we produce a refined version of the classical Pohozaev identity in the radial setting. The refined identity is then compared to the original, and possible applications are discussed.

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