Bulletin of the American Mathematical Society

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Book Information:

Authors: V. D. Kupradze, T. G. Gegelia, M. O. Basheleishvili and T. V. Burchuladze
Title: Three-dimensional problems of the mathematical theory of elasticity and thermoelasticity
Additional book information: Applied Mathematics and Mechanics, vol. 25, North-Holland, 1979, xix + 929 pp., $158.50.

1.

T. Boggio, Nuova risolutione di un problema fondamental delta teoria dell'elasticita, Atti Reale Accademia dei Lincei 16 (1907), 248-255.

2.

J. Boussinesq, Applications des potentiels à l'Etude de l'équilibre et du mouvement des solides élastiques, Gauthier-Villars, Paris, 1885.

3.

D. E. Carleson, Linear thermoelasticity, Handbuch der Physik Bd., VIa/2, 297-345, Springer-Verlag, Berlin, 1965.

4.

E. Cosserat and F. Cosserat, Sur les équations de la théorie de l'élasticité, Comptes Rendus de l'Acad. Sci. Paris 126 (1898), 1129-1132.

G. Duvaut and J.-L. Lions, Inequalities in mechanics and physics, Grundlehren der Mathematischen Wissenschaften, vol. 219, Springer-Verlag, Berlin-New York, 1976. Translated from the French by C. W. John. MR 0521262

A. Cemal Eringen, Nonlinear theory of continuous media, McGraw-Hill Book Co., New York-Toronto-London, 1962. MR 0191157

Gaetano Fichera, Sull’esistenza e sul calcolo delle soluzioni dei problemi al contorno, relativi all’equilibrio di un corpo elastico, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3) 4 (1950), no. 248, 35–99 = Consiglio Naz. Ricerche. Pubbl. Ist. Appl. Calcolo (1950) (Italian). MR 42040

Gaetano Fichera, Problemi elastostatici con vincoli unilaterali: Il problema di Signorini con ambigue condizioni al contorno, Atti Accad. Naz. Lincei Mem. Cl. Sci. Fis. Mat. Natur. Sez. Ia (8) 7 (1963/64), 91–140 (Italian). MR 178631

9.

G. Fichera, Existence theorems in elasticity, Handbuch der Physik, Bd. VIa/2, 347-389, Springer-Verlag, Berlin, 1972.

10.

G. Fichera, Boundary value problems of elasticity with unilateral constraints, Handbuch der Physik, Bd. VIa/2, 391-424, Springer-Verlag, Berlin, 1972.

G. Fichera, Homology spaces of $k$-measures and related inequalities for differential forms, Rend. Circ. Mat. Palermo (2) 26 (1977), no. 1-3, 52–54 (1978). MR 524332, DOI 10.1007/BF02854802

12.

I. Fredholm, Solution d'un problème fondamental de la théorie de l'elasticité, Ark. Mat. Astr. Fysik 2 (1906), 1-8.

13.

Galileo Galilei, Discorsi e dimonstrazioni matematiche, Leyden, 1638.

A. E. Green and W. Zerna, Theoretical elasticity, 2nd ed., Clarendon Press, Oxford, 1968. MR 0245245

15.

R. T. Gunther, Early science in Oxford, vol. 8, Clarendon Press, Oxford, 1931.

16.

M. E. Gurtin, The linear theory of elasticity, Handbuch der Physik VIa/2, 1-296, Springer-Verlag, Berlin, 1972.

17.

R. Hooke, Depotentia restitutiva, London, 1678.

18.

M. Kinoshita and T. Mura, On boundary value problems of elasticity, Research Report on the Faculty of Engineering, Meiji University 8 (1956), 56-82.

R. J. Knops and L. E. Payne, Uniqueness theorems in linear elasticity, Springer Tracts in Natural Philosophy, Vol. 19, Springer-Verlag, New York-Berlin, 1971. MR 0421244

Arthur Korn, Über die Lösung des Grundproblemes der Elastizitätstheorie, Math. Ann. 75 (1914), no. 4, 497–544 (German). MR 1511808, DOI 10.1007/BF01563656

V. D. Kupradze, Potential methods in the theory of elasticity, Israel Program for Scientific Translations, Jerusalem; Daniel Davey & Co., Inc., New York, 1965. Translated from the Russian by H. Gutfreund; Translation edited by I. Meroz. MR 0223128

22.

G. Lauricella, Sull'integrazione delle equazioni dell'equilibrio dei corpi elastici isotropi, Atti Reale Accademia dei Lincei 15 (1906), 426-432.

Leon Lichtenstein, Über die erste Randwertaufgabe der Elastizitätstheorie, Math. Z. 20 (1924), no. 1, 21–28 (German). MR 1544661, DOI 10.1007/BF01188070

J.-L. Lions and G. Stampacchia, Variational inequalities, Comm. Pure Appl. Math. 20 (1967), 493–519. MR 216344, DOI 10.1002/cpa.3160200302

25.

A. E. H. Love, A treatise on the mathematical theory of elasticity, (1st ed.), Cambridge Univ. Press, London, 1892 (4th ed. 1927).

26.

A. I. Lurie, Three-dimensional problems of elasticity, Gos. Izdat. Tech. Lit., Moscow, 1955; English transl. by D. B. McVean, Interscience Publishers, New York, 1964.

S. G. Mikhlin, Multidimensional singular integrals and integral equations, Pergamon Press, Oxford-New York-Paris, 1965. Translated from the Russian by W. J. A. Whyte; Translation edited by I. N. Sneddon. MR 0185399

28.

N. I. Muskhelishvili, Fundamental problems of the mathematical theory of elasticity (Russian), 5th ed., Gos. Izdat. Fiz.-Mat. Lit., Moscow, 1966; English transl. of 2nd ed. by J. R. L. Radok, Noordhoff Int. Publ. Co., Leyden.

29.

N. I. Muskhelishvili and G. G. Chernikh, Development of mechanics in the U.S.S.R. in the last fifty years (Russian), 3rd. Cong. Theor. Appl. Mech., Moscow, 1968.

Ian N. Sneddon, Fourier Transforms, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1951. MR 0041963

31.

I. N. Sneddon, The use of transform methods in elasticity, vol. 1, 1964; vol. 2, 1965, N.C. State University, Math. Dept.

Application of integral transforms in the theory of elasticity, International Centre for Mechanical Sciences, Courses and Lectures, No. 220, Springer-Verlag, Vienna-New York, 1975. Edited by I. N. Sneddon. MR 0502667

33.

I. Todhunter and K. Pearson, A history of the theory of elasticity and of the strength of materials, vol. 1, 1886; vol. 2, 1893, Cambridge Univ. Press, London.

C. Truesdell and W. Noll, The non-linear field theories of mechanics, Handbuch der Physik, Band III/3, Springer-Verlag, Berlin, 1965. MR 0193816

C. Truesdell and R. Toupin, The classical field theories, Handbuch der Physik, Bd. III/1, Springer, Berlin. With an appendix on tensor fields by J. L. Ericksen. MR 0118005

36.

Ya S. Uflyand, Integral transforms in the theory of elasticity (Russian) Akad. Nauk. Izdat., Leningrad, 1963.

Piero Villaggio, Qualitative methods in elasticity, Monographs and Textbooks on Mechanics of Solids and Fluids, Mechanics of Continua, Vol. 3, Noordhoff International Publishing, Leiden, 1977. MR 0502510

C. C. Wang and C. Truesdell, Introduction to rational elasticity, Monographs and Textbooks on Mechanics of Solids and Fluids, Mechanics of Continua, Noordhoff International Publishing, Leyden, 1973. MR 0468442

39.

C. C. Weyl, Das asymptotische Verteilungsgesetz der Eigenschwingungen eines beliebig gestalteten elastischen Körpers, Rend. Circ. Mat. Palermo 39 (1915), 1-49.

1.

T. Boggio, Nuova risolutione di un problema fondamental delta teoria dell'elasticita, Atti Reale Accademia dei Lincei 16 (1907), 248-255.

2.

J. Boussinesq, Applications des potentiels à l'Etude de l'équilibre et du mouvement des solides élastiques, Gauthier-Villars, Paris, 1885.

3.

D. E. Carleson, Linear thermoelasticity, Handbuch der Physik Bd., VIa/2, 297-345, Springer-Verlag, Berlin, 1965.

4.

E. Cosserat and F. Cosserat, Sur les équations de la théorie de l'élasticité, Comptes Rendus de l'Acad. Sci. Paris 126 (1898), 1129-1132.

5.

G. Duvaut and J. L. Lions, Les inéquations en mécanique et en physique, Dunod, Paris, 1972; English transl. by Charlotte W. John, Springer-Verlag, Berlin, 1976. MR 0521262

6.

A. C. Eringen, Non-linear theory of continuous media, McGraw-Hill, New York, 1962. MR 191157

7.

G. Fichera, Sull'esistenza e sul calcolo delle soluzioni dei problemi al contorno, relativi all'equilibria di un corpo elastico, Ann. Scuola Norm. Sup. Pisa 4 (1950), 36-99. MR 42040

8.

G. Fichera, Problemi elastostatici con vincoli unilaterali: il problema die Signorini con ambiguë condizioni al contorno, Mem. Accad. Naz. Lincei 8 (1964), 91-140. MR 178631

9.

G. Fichera, Existence theorems in elasticity, Handbuch der Physik, Bd. VIa/2, 347-389, Springer-Verlag, Berlin, 1972.

10.

G. Fichera, Boundary value problems of elasticity with unilateral constraints, Handbuch der Physik, Bd. VIa/2, 391-424, Springer-Verlag, Berlin, 1972.

11.

G. Fichera, II contriburo italiano alla teoria matematica dell'elasticità, Rend Circ. Mat Palermo 28 (1979), 5-26. MR 524332

12.

I. Fredholm, Solution d'un problème fondamental de la théorie de l'elasticité, Ark. Mat. Astr. Fysik 2 (1906), 1-8.

13.

Galileo Galilei, Discorsi e dimonstrazioni matematiche, Leyden, 1638.

14.

A. E. Green and W. Zerna, Theoretical elasticity, Clarendon Press, Oxford, 1954 (2nd ed. 1968). MR 245245

15.

R. T. Gunther, Early science in Oxford, vol. 8, Clarendon Press, Oxford, 1931.

16.

M. E. Gurtin, The linear theory of elasticity, Handbuch der Physik VIa/2, 1-296, Springer-Verlag, Berlin, 1972.

17.

R. Hooke, Depotentia restitutiva, London, 1678.

18.

M. Kinoshita and T. Mura, On boundary value problems of elasticity, Research Report on the Faculty of Engineering, Meiji University 8 (1956), 56-82.

19.

R. J. Knops and L. E. Payne, Uniqueness theorems in linear elasticity, Springer-Verlag, Berlin, 1971. MR 421244

20.

A. Korn, Über die Lösung des Grundproblems der Elastizitätstheorie, Math. Ann. 75 (1914), 497-549. MR 1511808

21.

V. D. Kupradze, Potential methods in the theory of elasticity (Russian), Gos. Izdat. Fiz-Mat Lit, Moscow, 1963; English transl. by H. Gutfreund, Israel Program for Scientific Translations, Jerusalem, 1965. MR 223128

22.

G. Lauricella, Sull'integrazione delle equazioni dell'equilibrio dei corpi elastici isotropi, Atti Reale Accademia dei Lincei 15 (1906), 426-432.

23.

L. Lichtenstein, Über die erste Randwertaufgabe der Elastizitätstheorie, Math. Z. 20 (1924), 21-28. MR 1544661

24.

J. L. Lions and G. Stampacchia, Variational inequalities, Comm. Pure Appl. Math. 20 (1967), 493-519. MR 216344

25.

A. E. H. Love, A treatise on the mathematical theory of elasticity, (1st ed.), Cambridge Univ. Press, London, 1892 (4th ed. 1927).

26.

A. I. Lurie, Three-dimensional problems of elasticity, Gos. Izdat. Tech. Lit., Moscow, 1955; English transl. by D. B. McVean, Interscience Publishers, New York, 1964.

27.

S. G. Mikhlin, Multidimensional singular integrals and integral equations (Russian), Gos. Izdat. Fiz.-Mat. Lit., Moscow, 1962; English transl. by W. J. A. Whyte, Pergamon Press, Oxford, 1965. MR 185399

28.

N. I. Muskhelishvili, Fundamental problems of the mathematical theory of elasticity (Russian), 5th ed., Gos. Izdat. Fiz.-Mat. Lit., Moscow, 1966; English transl. of 2nd ed. by J. R. L. Radok, Noordhoff Int. Publ. Co., Leyden.

29.

N. I. Muskhelishvili and G. G. Chernikh, Development of mechanics in the U.S.S.R. in the last fifty years (Russian), 3rd. Cong. Theor. Appl. Mech., Moscow, 1968.

30.

I. N. Sneddon, Fourier transforms, Chapter 10, McGraw-Hill, New York, 1951. MR 41963

31.

I. N. Sneddon, The use of transform methods in elasticity, vol. 1, 1964; vol. 2, 1965, N.C. State University, Math. Dept.

32.

I. N. Sneddon (ed.), Applications of integral transforms in the theory of elasticity, CISM Courses and Lectures No. 220, Springer-Verlag, Wien, 1977. MR 502667

33.

I. Todhunter and K. Pearson, A history of the theory of elasticity and of the strength of materials, vol. 1, 1886; vol. 2, 1893, Cambridge Univ. Press, London.

34.

C. Truesdell and W. Noll, The non-linear field theories of mechanics, Handbuch der Physik Bd. III/3, pp. 1-602, Springer-Verlag, Berlin, 1965. MR 193816

35.

C. Truesdell and R. Toupin, The classical field theories. With an Appendix on tensor fields, by J. L. Ericksen, Handbuch der Physik, Bd. III/l, pp. 226-793; appendix, pp. 794-858, Springer-Verlag, Berlin and New York, 1960. MR 118005

36.

Ya S. Uflyand, Integral transforms in the theory of elasticity (Russian) Akad. Nauk. Izdat., Leningrad, 1963.

37.

P. Villaggio, Qualitative methods in elasticity, Noordhoff Int. Publ. Co., Leyden, 1977. MR 502510

38.

C. C. Wang and C. Truesdell, Introduction to rational elasticity, Noordhoff Int. Publ. Co., Leyden, 1973. MR 468442

39.

C. C. Weyl, Das asymptotische Verteilungsgesetz der Eigenschwingungen eines beliebig gestalteten elastischen Körpers, Rend. Circ. Mat. Palermo 39 (1915), 1-49.