Function Spaces, Differential Operators and Nonlinear AnalysisLassi Päivärinta |
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A₁ analysis anisotropic applications assume assumptions Banach function space Banach spaces boundary value problems bounded coefficients compact complex consider constant continuous convex coordinate Corollary corresponding defined denote Department of Mathematics Dirichlet problem domain elliptic elliptic operators estimate EXAMPLE exists F₁ finite formula function f function spaces geometric Hankel operators Hardy inequality harmonic measure Hence Hilbert space Hölder inequality holds imbedding inequality integral interpolation invariant Kufner linear manifolds map f Math Nonlinear partial differential norm obtain Orlicz spaces partial differential equations Peetre polynomial projective structure proof properties Proposition pseudodifferential REMARK retraction satisfies semilinear singular smooth Sobolev mappings Sobolev spaces solution subset theorem theory topology transform V₁ V₂ w₁ wave equation weight functions weighted Sobolev spaces zero α α ερ