# Favorite Books

## Most favorite

*Mathematical Elasticity*by P.G.Ciarlet -- The notations on the website is based on this book.*Direct Methods in the Theory of Elliptic Equations*, by Necas,J.--Much written about Sobolev spaces defined in Lipschitz boundary*Elliptic Partial Differential Equations of Second Order*(1998) by Gilbarg, D. and Trudinger, N. S.-- Text book of PDEs*Sobolev Spaces 1st ed.*by Adams, R,A.-- Sobolev spaces defined on unbounded domains and iterpolations*Inequalities in Mechanics and Physics*, Duvaut, G. and Lions, J.L. --Book on continuum mechanics*Mathematical elasticity*Vol.1 -- 3D Elasticity by Ciarlet, P.G. -- My foundation on Elasticity*Elliptic Problems in Domains with Piecewise Smooth Boundaries*, by Nazarov, S.A. and Plamenevsky, B.A --Dealing with crack problems and J-integral (Cherepanov-Rice integral)*Non-Homogeneous Boundary Value Problems and Applications*, by J.L.Lions and E.Magenes -- Interpolations of Sobolev spaces*Singularities in Boundary Value Problems*by Grisvard, P. -- Introductory book on solutions of PDEs with singularity in domains with corner*Introduction fo Shape Sensitivity*by Sokolowski, J.and Zolesio, J.-P,--Introduction to shape sensitivity analysis
} *Nonlinear Functional Analysis and its Applications II/A*, by Zeidler. E. -- Linear Monotone Operators*Nonlinear Functional Analysis and its Applications III*, by Zeidler. E. -- Variational Methods and Optimization*Nonlinear Functional Analysis and its Applications IV,*, by Zeidler. E. -- Applications to Mathematical Physics

*Nonlinear Functional Analysis and its Applications II/B*, by Zeidler. E. -- Noninear Monotone Operators}

They are books that I often refer to, and many of them were read during graduate school. Most of them are purchased as electronic books or scanned and used.

## PDEs

*Functional Analysis*, by Yoshida K. -- Basic book of functional analysis*Solution of Variational Inequalities in Mechanics*, by Hlavacek.I. and J. Haslinger, J., Necas, J. and Lovlsek, J.-- Unilateral Problems, One-sided contact, Plasticity

## Continuum Mechanics and Shape Optimization

*Comception optimale de structures.pdf*, by Allaire, G.-- Numerical examples I used*Perturbation+Analysis+of+Optimization+Pr.pdf*, by Bonnans, J.F. and Shapiro, A.*Topological Derivatives in Shape Optimization*, by Novotny, A.A. and Sokolowski,J.-- Textbook of topological derivatives, Eshelby's*Topology Optimization*, by M.P. Bends$\phi $e, M.P. and Sigmund, O.-- Text about "What is topology optimization"*Shape sensitivity analysis via minmax differentiability*, by Delfour.M.C.ssnf . Zoléio -- Important paper to refer to when dealing with the Lagrange multiplier method*Homogenization and Porous Media*, by Allaire, G., Arbogast, T., Auriault, J.L. and Bourgeat. A.-- I want to target Porous Media in the future*Numerical analysis and optimization*, Allaire, G.-- Textbook*Thermal Stresses-Advanced Theory and Applications*, by Hetnarski, R.B. and Eslami, M.R.-- For the future*Topological Derivatives in Shape Optimization*by A.A.Novotny and J. Sokolowski-- 2.5 Eshelby Energy-Momentum Tensor

## Geometry

*Elementary Differential Geometry*, by Pressley, A.-- In 3-d fracture, Geodesic coordinates is used.

## Numerical Analysis (FEM)

*Finite element analysis using Mathematical programming language FreeFem++**in Japanese*,by Ohtsuka, K. and Takaishi, T.-- Basics of FreeFEM programming and applications to continuum mechanics, shape optimization by GJ-integral, reaction-diffusion system*Theory and Practice of FiniteElements*, Em, A. and Guermond,J.-L.-- From theory to notes on coding

## Fracture

*Fracture Mechanics - Inverse Problems and Solutions*, by Bui, H.D. -- Short summary of cracked materials, non-homogeneous materialss, composite materials, dissimilar interface, etc.*Mathematical and Computational Analyses of Cracking Formation*. by Sumi, Y. -- Theoretical researches in Fracture mechanics*Analysis of Cracks in Solids*, by Khludnev, A.M. and Kovtuenko, V.A.-- Variational methods in Crack problems*Multiscale modeling in continuum mechanics and structured deformations*, Energy Minimization for Isotropie Nonlinear Elastic Bodies by M. Silhavy; Variational Problems of Crack Equilibrium and Crack Propagation by Le,K.G; Griffith Theory Revisited by Marigo, J.-J.; Foundations of the Theory of Structured Deformations by Piero. G.D.; Second-Order Structured Deformations: Approximation Theorems by Paroni，R.; Crystalline Plasticity and Structured Deformations by Deseri, L.; Elastieity with Disarrangements by Owen, D.R.

## Shape optimization

*Shape Optimization Problems*by H.Azegami, H1-gradient method*Introduction fo Shape Sensitivity*by Sokolowski, J.and Zolesio, J.-P,--Hadamard formula*Optimal Shape Design for Elliptic Systems*by Olivier Pironneau

**Information about the page:** The current position is orange filled circle circle in the diagram below. Blue is the *My favorite books in Library* and **orange** is a duplicate for *public use*, where dashed line means the *intrface* to the Library in private.