Fuchsian reduction. Applications to geometry, cosmology and mathematical physics

zbMath1169.35002MaRDI QIDQ885340

Satyanad Kichenassamy

Publication date: 8 June 2007

Published in: Progress in Nonlinear Differential Equations and Their Applications (Search for Journal in Brave)

zbMATH Keywords

existencenonlinear wavesuniquenessnonlinear Schrödinger equationcosmologyHölder spacessolitoncosmological singularityconformal geometrypartial differential equationsTrudinger inequalityLiouville equationdistance functionHardy inequalityNash-Moser inverse function theoremGowdy spacetimesstellar modelsinterior Schauder estimatesChazy-equationClarke equationelliptic PDEs with boundary blowupFefferman-Graham metricsFuchsian problemsLoewner-Nirenberg metricsNirenberg examplenonlinear optics and laserssemilinear wavesspacetimes with twistweak detonations

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Nonlinear waves in solid mechanics (74J30) Shock waves and blast waves in fluid mechanics (76L05) Analyticity in context of PDEs (35A20) Combustion (80A25) Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory (83C20) Lasers, masers, optical bistability, nonlinear optics (78A60) PDEs in connection with relativity and gravitational theory (35Q75) Applications of local differential geometry to the sciences (53B50) Galactic and stellar dynamics (85A05) Research exposition (monographs, survey articles) pertaining to partial differential equations (35-02) Initial-boundary value problems for higher-order hyperbolic equations (35L35) Singularity in context of PDEs (35A21)

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