Displaying similar documents to “Complex powers of the wave operator.”

Dynamics of wave propagation and curvature of discriminants

Victor P. Palamodov (2000)

Annales de l'institut Fourier

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For a Lagrange distribution of order zero we consider a quadratic integral which has logarithmic divergence at the singular locus of the distribution. The residue of the asymptotics is a Hermitian form evaluated in the space of positive distributions supported in the locus. An asymptotic analysis of the residue density is given in terms of the curvature form of the locus. We state a conservation law for the residue of the impulse-energy tensor of solutions of the wave equation which...

On the Dirichlet and Neumann problems in multi-dimensional cone

Vladimir Vasilyev (2014)

Mathematica Bohemica

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We consider an elliptic pseudodifferential equation in a multi-dimensional cone, and using the wave factorization concept for an elliptic symbol we describe a general solution of such equation in Sobolev-Slobodetskii spaces. This general solution depends on some arbitrary functions, their quantity being determined by an index of the wave factorization. For identifying these arbitrary functions one needs some additional conditions, for example, boundary conditions. Simple boundary value...

The wave map problem. Small data critical regularity

Igor Rodnianski (2005-2006)

Séminaire Bourbaki

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The paper provides a description of the wave map problem with a specific focus on the breakthrough work of T. Tao which showed that a wave map, a dynamic lorentzian analog of a harmonic map, from Minkowski space into a sphere with smooth initial data and a small critical Sobolev norm exists globally in time and remains smooth. When the dimension of the base Minkowski space is ( 2 + 1 ) , the critical norm coincides with energy, the only manifestly conserved quantity in this (lagrangian) theory....