An Inverse Function Theorem in Sobolev Spaces and Applications to Quasi-Linear Schrödinger Equations
Copyright policy )An Inverse Function Theorem in Sobolev Spaces and Applications to Quasi-Linear Schrödinger Equations
An inverse function theorem of Nash-Moser type in Banach spaces with loss of derivatives is proved. The proof uses methods of Hörmanders result for Hölder spaces [\textit{L. Hörmander}, Arch. Ration. Mech. Anal. 62, 1-52 (1976; Zbl 0331.35020)] but this theorem applies to Sobolev spaces. Applications to non-linear evolution equations are given, e.g.~ a well-posedness result in Sobolev spaces for strongly singular quasi-linear Schrödinger equations.
- TU Dortmund University Germany
loss of derivatives, Derivatives of functions in infinite-dimensional spaces, Continuous and differentiable maps in nonlinear functional analysis, inverse function theorem of Nash-Moser type, Boundary value problems for second-order elliptic equations, inverse function theorem, global well posedness, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, Cauchy problem, quasi-linear Schrödinger equations, posedness, local well posedness, implicit function theorem, evolution equations, Applied Mathematics, nonlinear evolution equation, semigroup theory, Implicit function theorems; global Newton methods on manifolds, quasi-linear Schrödinger equation, Banach spaces, Sobolev spaces, Nash–Moser, Analysis
loss of derivatives, Derivatives of functions in infinite-dimensional spaces, Continuous and differentiable maps in nonlinear functional analysis, inverse function theorem of Nash-Moser type, Boundary value problems for second-order elliptic equations, inverse function theorem, global well posedness, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, Cauchy problem, quasi-linear Schrödinger equations, posedness, local well posedness, implicit function theorem, evolution equations, Applied Mathematics, nonlinear evolution equation, semigroup theory, Implicit function theorems; global Newton methods on manifolds, quasi-linear Schrödinger equation, Banach spaces, Sobolev spaces, Nash–Moser, Analysis
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