Garcke, Harald; Hecht, Claudia Shape and topology optimization in Stokes flow with a phase field approach. (English) Zbl 1334.49133 Appl. Math. Optim. 73, No. 1, 23-70 (2016). MSC: 49Q10 49Q20 35R35 35Q35 76D07 PDF BibTeX XML Cite \textit{H. Garcke} and \textit{C. Hecht}, Appl. Math. Optim. 73, No. 1, 23--70 (2016; Zbl 1334.49133) Full Text: DOI
Chakib, A.; Nachaoui, A.; Nachaoui, M. Existence analysis of an optimal shape design problem with non coercive state equation. (English) Zbl 1327.49070 Nonlinear Anal., Real World Appl. 28, 171-183 (2016). MSC: 49Q10 35R35 PDF BibTeX XML Cite \textit{A. Chakib} et al., Nonlinear Anal., Real World Appl. 28, 171--183 (2016; Zbl 1327.49070) Full Text: DOI
Garcke, Harald; Hecht, Claudia A phase field approach for shape and topology optimization in Stokes flow. (English) Zbl 1329.76108 Pratelli, Aldo (ed.) et al., New trends in shape optimization. Cham: Birkhäuser/Springer (ISBN 978-3-319-17562-1/hbk; 978-3-319-17563-8/ebook). ISNM. International Series of Numerical Mathematics 166, 103-115 (2015). MSC: 76D55 49Q10 76S05 PDF BibTeX XML Cite \textit{H. Garcke} and \textit{C. Hecht}, ISNM, Int. Ser. Numer. Math. 166, 103--115 (2015; Zbl 1329.76108) Full Text: DOI
Delfour, Michel C. Metric spaces of shapes and geometries constructed from set parametrized functions. (English) Zbl 1329.49084 Pratelli, Aldo (ed.) et al., New trends in shape optimization. Cham: Birkhäuser/Springer (ISBN 978-3-319-17562-1/hbk; 978-3-319-17563-8/ebook). ISNM. International Series of Numerical Mathematics 166, 57-101 (2015). MSC: 49Q10 PDF BibTeX XML Cite \textit{M. C. Delfour}, ISNM, Int. Ser. Numer. Math. 166, 57--101 (2015; Zbl 1329.49084) Full Text: DOI
Snelson, Stanley Regularity and long-time behavior of nonlocal heat flows. (English) Zbl 1333.35103 Calc. Var. Partial Differ. Equ. 54, No. 2, 1705-1723 (2015). Reviewer: Giuseppe Buttazzo (Pisa) MSC: 35K55 49N60 35B40 35B25 PDF BibTeX XML Cite \textit{S. Snelson}, Calc. Var. Partial Differ. Equ. 54, No. 2, 1705--1723 (2015; Zbl 1333.35103) Full Text: DOI arXiv
Kupenko, Olha P.; Manzo, Rosanna Shape stability of optimal control problems in coefficients for coupled system of Hammerstein type. (English) Zbl 1326.49007 Discrete Contin. Dyn. Syst., Ser. B 20, No. 9, 2967-2992 (2015). MSC: 49J20 49J45 49K40 35J57 93C73 PDF BibTeX XML Cite \textit{O. P. Kupenko} and \textit{R. Manzo}, Discrete Contin. Dyn. Syst., Ser. B 20, No. 9, 2967--2992 (2015; Zbl 1326.49007) Full Text: DOI arXiv
Varchon, Nicolas Domain perturbation and invariant manifolds. (English) Zbl 1257.35024 J. Evol. Equ. 12, No. 3, 547-569 (2012). MSC: 35B20 35K58 35B35 35B42 35K20 35K57 PDF BibTeX XML Cite \textit{N. Varchon}, J. Evol. Equ. 12, No. 3, 547--569 (2012; Zbl 1257.35024) Full Text: DOI
He, Y.; Guo, B. Z. The existence of optimal solution for a shape optimization problem on starlike domain. (English) Zbl 1239.90104 J. Optim. Theory Appl. 152, No. 1, 21-30 (2012). Reviewer: Vasile Postolică (Piatra Neamt) MSC: 90C48 90C56 PDF BibTeX XML Cite \textit{Y. He} and \textit{B. Z. Guo}, J. Optim. Theory Appl. 152, No. 1, 21--30 (2012; Zbl 1239.90104) Full Text: DOI
Buttazzo, Giuseppe Spectral optimization problems. (English) Zbl 1226.49038 Rev. Mat. Complut. 24, No. 2, 277-322 (2011). MSC: 49Q20 49R05 35P15 47A75 35J25 PDF BibTeX XML Cite \textit{G. Buttazzo}, Rev. Mat. Complut. 24, No. 2, 277--322 (2011; Zbl 1226.49038) Full Text: DOI arXiv
Tan, Zhong; Zhang, Ying Hui Shape optimization in two-dimensional viscous compressible fluids. (English) Zbl 1206.35033 Acta Math. Sin., Engl. Ser. 26, No. 9, 1793-1806 (2010). Reviewer: Gelu Paşa (Bucureşti) MSC: 35B30 35Q30 PDF BibTeX XML Cite \textit{Z. Tan} and \textit{Y. H. Zhang}, Acta Math. Sin., Engl. Ser. 26, No. 9, 1793--1806 (2010; Zbl 1206.35033) Full Text: DOI
Helffer, B.; Hoffmann-Ostenhof, T.; Terracini, S. Nodal domains and spectral minimal partitions. (English) Zbl 1171.35083 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 26, No. 1, 101-138 (2009). Reviewer: Ruxandra Stavre (Bucureşti) MSC: 35P05 35J10 35B65 PDF BibTeX XML Cite \textit{B. Helffer} et al., Ann. Inst. Henri Poincaré, Anal. Non Linéaire 26, No. 1, 101--138 (2009; Zbl 1171.35083) Full Text: DOI EuDML arXiv
Caffarelli, L. A.; Lin, Fang-Hua Singularly perturbed elliptic systems and multi-valued harmonic functions with free boundaries. (English) Zbl 1194.35138 J. Am. Math. Soc. 21, No. 3, 847-862 (2008). MSC: 35J57 35B25 35P30 35B65 31B05 PDF BibTeX XML Cite \textit{L. A. Caffarelli} and \textit{F.-H. Lin}, J. Am. Math. Soc. 21, No. 3, 847--862 (2008; Zbl 1194.35138) Full Text: DOI
Wang, Gengsheng; Yang, Donghui Decomposition of vector-valued divergence free Sobolev functions and shape optimization for stationary Navier-Stokes equations. (English) Zbl 1141.49038 Commun. Partial Differ. Equations 33, No. 3, 429-449 (2008). MSC: 49Q10 35B37 35Q30 PDF BibTeX XML Cite \textit{G. Wang} and \textit{D. Yang}, Commun. Partial Differ. Equations 33, No. 3, 429--449 (2008; Zbl 1141.49038) Full Text: DOI arXiv
Cafferelli, L. A.; Lin, Fang Hua An optimal partition problem for eigenvalues. (English) Zbl 1123.65060 J. Sci. Comput. 31, No. 1-2, 5-18 (2007). Reviewer: Gerald W. Hedstrom (Pleasanton) MSC: 65K10 35J05 49J30 65N25 PDF BibTeX XML Cite \textit{L. A. Cafferelli} and \textit{F. H. Lin}, J. Sci. Comput. 31, No. 1--2, 5--18 (2007; Zbl 1123.65060) Full Text: DOI
Bucur, Dorin Characterization of the shape stability for nonlinear elliptic problems. (English) Zbl 1245.35035 J. Differ. Equations 226, No. 1, 99-117 (2006). MSC: 35J60 31C45 35B35 PDF BibTeX XML Cite \textit{D. Bucur}, J. Differ. Equations 226, No. 1, 99--117 (2006; Zbl 1245.35035) Full Text: DOI
Chenais, D.; Zuazua, Enrique Finite-element approximation of 2D elliptic optimal design. (English) Zbl 1086.49027 J. Math. Pures Appl., IX. Sér. 85, No. 2, 225-249 (2006). MSC: 49Q10 49M25 35J05 65M60 PDF BibTeX XML Cite \textit{D. Chenais} and \textit{E. Zuazua}, J. Math. Pures Appl. (9) 85, No. 2, 225--249 (2006; Zbl 1086.49027) Full Text: DOI
Barkatou, Mohammed; Seck, Diaraf; Ly, Idrissa An existence result for a quadrature surface free boundary problem. (English) Zbl 1207.35106 Cent. Eur. J. Math. 3, No. 1, 39-57 (2005). MSC: 35J05 35A35 PDF BibTeX XML Cite \textit{M. Barkatou} et al., Cent. Eur. J. Math. 3, No. 1, 39--57 (2005; Zbl 1207.35106) Full Text: DOI Link
Ly, Idrissa; Seck, Diaraf Shape optimization and free boundary problem: the case of the \(p\)-Laplacian. (Optimisation de forme et problème à frontière libre: cas du \(p\)-laplacien.) (French) Zbl 1050.35153 Ann. Fac. Sci. Toulouse, VI. Sér., Math. 12, No. 1, 103-126 (2003). Reviewer: Alain Brillard (Mulhouse) MSC: 35R35 35J65 49Q10 PDF BibTeX XML Cite \textit{I. Ly} and \textit{D. Seck}, Ann. Fac. Sci. Toulouse, Math. (6) 12, No. 1, 103--126 (2003; Zbl 1050.35153) Full Text: DOI Numdam EuDML
Savaré, Giuseppe; Schimperna, Giulio Domain perturbations and estimates for the solutions of second order elliptic equations. (English) Zbl 1112.35312 J. Math. Pures Appl. (9) 81, No. 11, 1071-1112 (2002). Reviewer: Ruxandra Stavre (Bucureşti) MSC: 35J20 35B30 35J25 PDF BibTeX XML Cite \textit{G. Savaré} and \textit{G. Schimperna}, J. Math. Pures Appl. (9) 81, No. 11, 1071--1112 (2002; Zbl 1112.35312) Full Text: DOI
Feireisl, Eduard; Novotný, Antonín; Petzeltová, Hana On the domain dependence of solutions to the compressible Navier-Stokes equations of a barotropic fluid. (English) Zbl 0996.35051 Math. Methods Appl. Sci. 25, No. 12, 1045-1073 (2002). MSC: 35Q30 35B30 76N10 35D05 PDF BibTeX XML Cite \textit{E. Feireisl} et al., Math. Methods Appl. Sci. 25, No. 12, 1045--1073 (2002; Zbl 0996.35051) Full Text: DOI
Bucur, Dorin; Varchon, Nicolas Boundary variation for a Neumann problem. (English) Zbl 1072.35063 Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 29, No. 4, 807-821 (2000). Reviewer: Leszek Gasiński (Kraków) MSC: 35J20 35B20 35J25 PDF BibTeX XML Cite \textit{D. Bucur} and \textit{N. Varchon}, Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 29, No. 4, 807--821 (2000; Zbl 1072.35063) Full Text: Numdam EuDML
Bucur, Dorin Characterization for the Kuratowski limits of a sequence of Sobolev spaces. (English) Zbl 0924.46028 J. Differ. Equations 151, No. 1, 1-19 (1999). Reviewer: H.Triebel (Jena) MSC: 46E35 PDF BibTeX XML Cite \textit{D. Bucur}, J. Differ. Equations 151, No. 1, 1--19 (1999; Zbl 0924.46028) Full Text: DOI
Holzleitner, L. Improvements on objective and constrain functions in domain optimization. (English) Zbl 0962.74047 Comput. Methods Appl. Mech. Eng. 163, No. 1-4, 271-291 (1998). MSC: 74P10 74S05 PDF BibTeX XML Cite \textit{L. Holzleitner}, Comput. Methods Appl. Mech. Eng. 163, No. 1--4, 271--291 (1998; Zbl 0962.74047) Full Text: DOI
Bucur, Dorin; Trebeschi, Paola Shape optimisation problems governed by nonlinear state equations. (English) Zbl 0918.49030 Proc. R. Soc. Edinb., Sect. A, Math. 128, No. 5, 945-963 (1998). Reviewer: R.De Arcangelis (Napoli) MSC: 49Q10 49J20 PDF BibTeX XML Cite \textit{D. Bucur} and \textit{P. Trebeschi}, Proc. R. Soc. Edinb., Sect. A, Math. 128, No. 5, 945--963 (1998; Zbl 0918.49030) Full Text: DOI
Barkatou, Mohammed; Henrot, Antoine An existence result in shape optimization using a geometric property of the normal vector. (Un résultat d’existence en optimisation de forme en utilisant une propriété géométrique de la normale.) (French) Zbl 0920.49027 ESAIM, Control Optim. Calc. Var. 2, 105-123 (1997). Reviewer: B.Kawohl (Köln) MSC: 49Q10 49K99 49J40 PDF BibTeX XML Cite \textit{M. Barkatou} and \textit{A. Henrot}, ESAIM, Control Optim. Calc. Var. 2, 105--123 (1997; Zbl 0920.49027) Full Text: DOI Link EuDML
Bucur, D. Shape analysis for nonsmooth elliptic operators. (English) Zbl 0874.49035 Appl. Math. Lett. 9, No. 3, 11-16 (1996). MSC: 49Q10 35J15 31B35 35D10 PDF BibTeX XML Cite \textit{D. Bucur}, Appl. Math. Lett. 9, No. 3, 11--16 (1996; Zbl 0874.49035) Full Text: DOI