메뉴 건너뛰기




Volumn 2, Issue 3, 2002, Pages 365-382

Structure of shape derivatives

Author keywords

Derivatives; Free boundary; Manifolds; Nonlinear partial differential equations; Optimization; Shapes; Variational calculus

Indexed keywords


EID: 0346367651     PISSN: 14243199     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00028-002-8093-y     Document Type: Article
Times cited : (65)

References (20)
  • 1
    • 0011843163 scopus 로고    scopus 로고
    • Anatomy of the Shape Hessian Via Lie Brackets
    • BUCUR, D. and ZOLÉSIO, J. P., Anatomy of the Shape Hessian Via Lie Brackets, Annali di Mat. Pura ed Appl. (IV), vol. CLXXIII (1997), 127-143.
    • (1997) Annali di Mat. Pura ed Appl. (IV) , vol.173 , pp. 127-143
    • Bucur, D.1    Zolésio, J.P.2
  • 2
    • 0000339040 scopus 로고
    • Problems of Shape Optimal Design
    • Haug and Céa (eds) Sijthoff & Noordhoff, Alphen aan den Rijn
    • CÉA, J., Problems of Shape Optimal Design, in Haug and Céa (eds), Optimization of Distributed Parameters Structures, Part II, Sijthoff & Noordhoff, Alphen aan den Rijn. 1981.
    • (1981) Optimization of Distributed Parameters Structures , Issue.2 PART
    • Céa, J.1
  • 3
    • 0034375072 scopus 로고    scopus 로고
    • About stability of equilibrium shapes
    • DAMBRINE, M. and PIERRE, M., About stability of equilibrium shapes. M2AN, vol. 34 (2000) no. 4, 811-834.
    • (2000) M2AN , vol.34 , Issue.4 , pp. 811-834
    • Dambrine, M.1    Pierre, M.2
  • 4
    • 0040298755 scopus 로고
    • A stability result for the magnetic shaping problem
    • DESCLOUX, J., A stability result for the magnetic shaping problem. Z. Angew. Math. Phys. 45(4) (1994), 543-555.
    • (1994) Z. Angew. Math. Phys. , vol.45 , Issue.4 , pp. 543-555
    • Descloux, J.1
  • 5
    • 0026254180 scopus 로고
    • Velocity Method and Lagrangian Formulation for the Computation of the Shape Hessian
    • DELFOUR, C. M. and ZOLÉSIO, J. P., Velocity Method and Lagrangian Formulation for the Computation of the Shape Hessian. SIAM Control and Optimization 29(6) (1991), 1414-1442.
    • (1991) SIAM Control and Optimization , vol.29 , Issue.6 , pp. 1414-1442
    • Delfour, C.M.1    Zolésio, J.P.2
  • 7
    • 0348095865 scopus 로고    scopus 로고
    • Fréchet-Differentiability and Sufficient Optimality Conditions for Shape Functionals
    • K-H. Hoffmann, G. Leugering, F. Tröltzsch ed. Birkhäuser
    • EPPLER, K., Fréchet-Differentiability and Sufficient Optimality Conditions for Shape Functionals. In: Optimal control of Partial Differential Equations, K-H. Hoffmann, G. Leugering, F. Tröltzsch ed., vol. 133 (1999), 133-143, Birkhäuser.
    • (1999) Optimal Control of Partial Differential Equations , vol.133 , pp. 133-143
    • Eppler, K.1
  • 8
    • 0034401181 scopus 로고    scopus 로고
    • Second Derivatives and Sufficient Optimality Conditions for Shape Functionals
    • To appear
    • EPPLER, K., Second Derivatives and Sufficient Optimality Conditions for Shape Functionals. To appear in Control and Cybernetics.
    • Control and Cybernetics
    • Eppler, K.1
  • 9
    • 0025432278 scopus 로고
    • Second order necessary conditions in a domain optimization problem
    • FUJII, N., Second order necessary conditions in a domain optimization problem. Journal of Optimization Theory and Applications, vol. 65 (1990) no. 2, 223-245.
    • (1990) Journal of Optimization Theory and Applications , vol.65 , Issue.2 , pp. 223-245
    • Fujii, N.1
  • 10
    • 0347465917 scopus 로고
    • Sufficient conditions for optimality in shape optimization
    • FUJII, N., Sufficient conditions for optimality in shape optimization. Control and Cybernetics, vol. 23 (1994) no. 3, 393-406.
    • (1994) Control and Cybernetics , vol.23 , Issue.3 , pp. 393-406
    • Fujii, N.1
  • 11
    • 0348095864 scopus 로고
    • A Potential Method for Shape Optimization problems
    • FUJII, N. and GOTO, Y., A Potential Method for Shape Optimization problems. Control and Cybernetics, vol. 23 (1994) no. 3, 383-392.
    • (1994) Control and Cybernetics , vol.23 , Issue.3 , pp. 383-392
    • Fujii, N.1    Goto, Y.2
  • 19
    • 0001351887 scopus 로고
    • Differentiation with respect to the domain in boundary value problems
    • SIMON, J., Differentiation with respect to the domain in boundary value problems, Numer. Funct. Anal. and Optimiz., vol. 2 (1980) no. 7 and 8, 649-687.
    • (1980) Numer. Funct. Anal. and Optimiz. , vol.2 , Issue.7-8 , pp. 649-687
    • Simon, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.