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Dynamics of wave propagation and curvature of discriminants

Victor P. Palamodov (2000)

Annales de l'institut Fourier

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 extends the...

Generating singularities of solutions of quasilinear elliptic equations using Wolff’s potential

Darko Žubrinić (2003)

Czechoslovak Mathematical Journal

We consider a quasilinear elliptic problem whose left-hand side is a Leray-Lions operator of p -Laplacian type. If p < γ < N and the right-hand side is a Radon measure with singularity of order γ at x 0 ∈ Ω , then any supersolution in W l o c 1 , p ( Ω ) has singularity of order at least ( γ - p ) ( p - 1 ) at x 0 . In the proof we exploit a pointwise estimate of 𝒜 -superharmonic solutions, due to Kilpeläinen and Malý, which involves Wolff’s potential of Radon’s measure.

Global time estimates for solutions to equations of dissipative type

Michael Ruzhansky, James Smith (2005)

Journées Équations aux dérivées partielles

Global time estimates of L p - L q norms of solutions to general strictly hyperbolic partial differential equations are considered. The case of special interest in this paper are equations exhibiting the dissipative behaviour. Results are applied to discuss time decay estimates for Fokker-Planck equations and for wave type equations with negative mass.

Harmonic metrics and connections with irregular singularities

Claude Sabbah (1999)

Annales de l'institut Fourier

We identify the holomorphic de Rham complex of the minimal extension of a meromorphic vector bundle with connexion on a compact Riemann surface X with the L 2 complex relative to a suitable metric on the bundle and a complete metric on the punctured Riemann surface. Applying results of C. Simpson, we show the existence of a harmonic metric on this vector bundle, giving the same L 2 complex.

Currently displaying 41 – 60 of 198