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Functional Analysis, Sobolev Spaces and Partial Differential Equations
TLDR
In this article, the theory of conjugate convex functions is introduced, and the Hahn-Banach Theorem and the closed graph theorem are discussed, as well as the variations of boundary value problems in one dimension.Abstract:
Preface.- 1. The Hahn-Banach Theorems. Introduction to the Theory of Conjugate Convex Functions.- 2. The Uniform Boundedness Principle and the Closed Graph Theorem. Unbounded Operators. Adjoint. Characterization of Surjective Operators.- 3. Weak Topologies. Reflexive Spaces. Separable Spaces. Uniform Convexity.- 4. L^p Spaces.- 5. Hilbert Spaces.- 6. Compact Operators. Spectral Decomposition of Self-Adjoint Compact Operators.- 7. The Hille-Yosida Theorem.- 8. Sobolev Spaces and the Variational Formulation of Boundary Value Problems in One Dimension.- 9. Sobolev Spaces and the Variational Formulation of Elliptic Boundary Value Problems in N Dimensions.- 10. Evolution Problems: The Heat Equation and the Wave Equation.- 11. Some Complements.- Problems.- Solutions of Some Exercises and Problems.- Bibliography.- Index.read more
Citations
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Journal ArticleDOI
A Theory of Super-Resolution from Short-Time Fourier Transform Measurements
TL;DR: A theory of super-resolution from short-time Fourier transform (STFT) measurements is developed and it is proved that the correct solution can be approximated—in weak-* topology—by solving a sequence of finite-dimensional convex programming problems.
Dissertation
Qualitative methods for heterogeneous media
TL;DR: In this paper, the authors focus on non destructive testing of concrete using ultrasonic waves, and thus examine imaging in complex heterogeneous media, where measurements are multistatic, which means that we record the total measurements on different points by using several sources.
Journal ArticleDOI
A priori estimates for some elliptic equations involving the p-Laplacian
Lucio Damascelli,Rosa Pardo +1 more
TL;DR: In this paper, the Dirichlet problem for positive solutions of the equation − Δ p ( u) = f ( u ) in a convex, bounded, smooth domain Ω ⊂ R N, with f locally Lipschitz continuous was considered.
Journal ArticleDOI
Dynamical analysis and optimal control simulation for an age-structured cholera transmission model
TL;DR: An age-structured cholera model is proposed that incorporates both the environment-to-human and human- to-human transmission pathways and that includes host vaccination and water sanitation as disease control measures and rigorously investigates the threshold dynamics of this model using the basic reproduction number derived from the analysis.
Posted Content
A microscopic model for a one parameter class of fractional laplacians with dirichlet boundary conditions
TL;DR: In this paper, the hydrodynamic limit for the symmetric exclusion process with long jumps given by a mean zero probability transition rate with infinite variance and in contact with infinitely many reservoirs with density ρ$ at the left of the system and π$ at β$ on the right of system is shown.
References
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Book
Linear and Quasilinear Equations of Parabolic Type
TL;DR: In this article, the authors considered a hyperbolic parabolic singular perturbation problem for a quasilinear equation of kirchhoff type and obtained parameter dependent time decay estimates of the difference between the solutions of the solution of a quasi-linear parabolic equation and the corresponding linear parabolic equations.
Book
Non-homogeneous boundary value problems and applications
TL;DR: In this paper, the authors consider the problem of finding solutions to elliptic boundary value problems in Spaces of Analytic Functions and of Class Mk Generalizations in the case of distributions and Ultra-Distributions.
Book
Introduction to Fourier Analysis on Euclidean Spaces.
Elias M. Stein,Guido Weiss +1 more
TL;DR: In this paper, the authors present a unified treatment of basic topics that arise in Fourier analysis, and illustrate the role played by the structure of Euclidean spaces, particularly the action of translations, dilatations, and rotations.
Book
Theory of function spaces
TL;DR: In this article, the authors measure smoothness using Atoms and Pointwise Multipliers, Wavelets, Spaces on Lipschitz Domains, Wavelet and Sampling Numbers.