Bethuel, Fabrice A counterexample to the weak density of smooth maps between manifolds in Sobolev spaces. (English) Zbl 1433.58009 Invent. Math. 219, No. 2, 507-651 (2020). Reviewer: Hirokazu Nishimura (Tsukuba) MSC: 58C25 46E35 82D15 PDFBibTeX XMLCite \textit{F. Bethuel}, Invent. Math. 219, No. 2, 507--651 (2020; Zbl 1433.58009) Full Text: DOI arXiv
Bethuel, Fabrice Asymptotics for two-dimensional vectorial Allen-Cahn systems. arXiv:2003.10189 Preprint, arXiv:2003.10189 [math.AP] (2020). BibTeX Cite \textit{F. Bethuel}, ``Asymptotics for two-dimensional vectorial Allen-Cahn systems'', Preprint, arXiv:2003.10189 [math.AP] (2020) Full Text: arXiv OA License
Bethuel, Fabrice Concentration sets for multiple equal-depth wells potentials in the 2D elliptic case. arXiv:1802.01333 Preprint, arXiv:1802.01333 [math.AP] (2018). MSC: 35B25 BibTeX Cite \textit{F. Bethuel}, ``Concentration sets for multiple equal-depth wells potentials in the 2D elliptic case'', Preprint, arXiv:1802.01333 [math.AP] (2018) Full Text: arXiv OA License
Bethuel, Fabrice A new obstruction to the extension problem for Sobolev maps between manifolds. (English) Zbl 1321.46035 J. Fixed Point Theory Appl. 15, No. 1, 155-183 (2014). MSC: 46E35 46T30 58D15 PDFBibTeX XMLCite \textit{F. Bethuel}, J. Fixed Point Theory Appl. 15, No. 1, 155--183 (2014; Zbl 1321.46035) Full Text: DOI arXiv
Bethuel, Fabrice The Jacobian, the square root and the set \(\infty \). (English) Zbl 1173.35038 J. Math. Anal. Appl. 352, No. 1, 548-572 (2009). MSC: 35F20 PDFBibTeX XMLCite \textit{F. Bethuel}, J. Math. Anal. Appl. 352, No. 1, 548--572 (2009; Zbl 1173.35038) Full Text: DOI
Béthuel, Fabrice Vortex dynamics of the parabolic Ginzburg-Landau equation. (Dynamique des tourbillons de vorticité pour l’équation de Ginzurg-Landau parabolique.) (French) Zbl 1178.35002 Sémin. Équ. Dériv. Partielles, Éc. Polytech., Cent. Math. Laurent Schwartz, Palaiseau 2006-2007, Exp. No. XVIII, 16 p. (2007). Reviewer: Vicenţiu D. Rădulescu (Craiova) MSC: 35-02 35B40 35B25 35K55 82D55 PDFBibTeX XMLCite \textit{F. Béthuel}, Sémin. Équ. Dériv. Partielles, Éc. Polytech., Cent. Math. Laurent Schwartz, Palaiseau 2006--2007, Exp. No. XVIII, 16 p. (2007; Zbl 1178.35002)
Bethuel, F. Variational methods for Ginzburg-Landau equations. (English) Zbl 0940.35073 Hildebrandt, S. (ed.) et al., Calculus of variations and geometric evolution problems. Lectures given at the 2nd session of the Centro Internazionale Matematico Estivo (CIME), Cetraro, Italy, June 15-22, 1996. Berlin: Springer. Lect. Notes Math. 1713, 1-43 (1999). Reviewer: Vicentiu D.Rădulescu (Craiova) MSC: 35J50 35B40 35J55 47J30 49J35 58E05 PDFBibTeX XMLCite \textit{F. Bethuel}, Lect. Notes Math. 1713, 1--43 (1999; Zbl 0940.35073)
Bethuel, F. Some recent results for the Ginzburg-Landau equation. (English) Zbl 0908.35047 Balog, A. (ed.) et al., European congress of mathematics (ECM), Budapest, Hungary, July 22–26, 1996. Volume I. Basel: Birkhäuser. Prog. Math. 168, 92-99 (1998). MSC: 35J65 35J20 82D55 35B05 PDFBibTeX XMLCite \textit{F. Bethuel}, Prog. Math. 168, 92--99 (1998; Zbl 0908.35047)
Bethuel, Fabrice Vortices in Ginzburg-Landau equations. (English) Zbl 0896.35044 Doc. Math., Extra Vol. ICM Berlin 1998, vol. III, 11-19 (1998). MSC: 35J65 35B05 35Q35 35Q55 82D50 82D55 35J20 PDFBibTeX XMLCite \textit{F. Bethuel}, Doc. Math. Extra Vol., 11--19 (1998; Zbl 0896.35044) Full Text: EuDML EMIS
Bethuel, Fabrice Approximations in trace spaces defined between manifolds. (English) Zbl 0824.58011 Nonlinear Anal., Theory Methods Appl. 24, No. 1, 121-130 (1995). Reviewer: Th.M.Rassias (Athens) MSC: 58C25 PDFBibTeX XMLCite \textit{F. Bethuel}, Nonlinear Anal., Theory Methods Appl. 24, No. 1, 121--130 (1995; Zbl 0824.58011) Full Text: DOI
Bethuel, Fabrice Some applications of the coarea formula to partial differential equations. (English) Zbl 0879.35028 Pràstaro, A. (ed.) et al., Geometry in partial differential equations. Singapore: World Scientific. 1-17 (1994). MSC: 35B45 49Q15 28A75 58C35 PDFBibTeX XMLCite \textit{F. Bethuel}, in: Geometry in partial differential equations. Singapore: World Scientific. 1--17 (1994; Zbl 0879.35028)
Bethuel, Fabrice Weak limits of Palais-Smale sequences for a class of critical functionals. (English) Zbl 0812.58018 Calc. Var. Partial Differ. Equ. 1, No. 3, 267-310 (1993). Reviewer: R.N.Kaul (Delhi) MSC: 58E20 49J45 58E05 PDFBibTeX XMLCite \textit{F. Bethuel}, Calc. Var. Partial Differ. Equ. 1, No. 3, 267--310 (1993; Zbl 0812.58018) Full Text: DOI
Bethuel, Fabrice On the singular set of stationary harmonic maps. (English) Zbl 0792.53039 Manuscr. Math. 78, No. 4, 417-443 (1993). Reviewer: J.Eells (Cambridge) MSC: 53C20 58E20 PDFBibTeX XMLCite \textit{F. Bethuel}, Manuscr. Math. 78, No. 4, 417--443 (1993; Zbl 0792.53039) Full Text: DOI EuDML
Bethuel, Fabrice Un résultat de régularité pour les solutions de l’équation des surfaces à courboure moyenne prescrite. (A regularity result for solutions of the equation of surfaces of prescribed mean curvature). (French. Abridged English version) Zbl 0795.35024 C. R. Acad. Sci., Paris, Sér. I 314, No. 13, 1003-1007 (1992). MSC: 35J60 53C21 53A10 35D10 35B45 35R45 PDFBibTeX XMLCite \textit{F. Bethuel}, C. R. Acad. Sci., Paris, Sér. I 314, No. 13, 1003--1007 (1992; Zbl 0795.35024)
Bethuel, Fabrice The approximation problem for Sobolev maps between two manifolds. (English) Zbl 0756.46017 Acta Math. 167, No. 3-4, 153-206 (1991). Reviewer: C.S.Sharma (London) MSC: 46E35 58D15 54C35 PDFBibTeX XMLCite \textit{F. Bethuel}, Acta Math. 167, No. 3--4, 153--206 (1991; Zbl 0756.46017) Full Text: DOI
Bethuel, Fabrice Passage à la limite faible dans des équations aux dérivées partielles non linéaires. (Passing to the weak limit in nonlinear partial differential equations). (French) Zbl 0751.35001 Journ. Équ. Dériv. Partielles, St.-Jean-De-Monts 1991, No.III, 12 p. (1991). Reviewer: X.-P.Wang (Nantes) MSC: 35A15 35J60 PDFBibTeX XML Full Text: Numdam EuDML
Bethuel, Fabrice Approximation in Sobolev spaces between two manifolds and homotopy groups. (English) Zbl 0734.46022 Variational methods, Proc. Conf., Paris/Fr. 1988, Prog. Nonlinear Differ. Equ. Appl. 4, 239-249 (1990). MSC: 46E35 58E20 41A65 PDFBibTeX XML
Béthuel, F. Energies relaxées pour applications harmoniques. (Relaxed energies for harmonic maps). (French) Zbl 0722.35031 Sémin. Équations Dériv. Partielles 1989-1990, No. 15, 9 p. (1990). Reviewer: M.Cinquini-Cibrario (Pavia) MSC: 35J20 PDFBibTeX XML Full Text: Numdam EuDML
Bethuel, F. A characterization of maps in \(H^ 1(B^ 3,S^ 2)\) which can be approximated by smooth maps. (English) Zbl 0708.58004 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 7, No. 4, 269-286 (1990). Reviewer: J.Durdil MSC: 58C25 46E35 PDFBibTeX XMLCite \textit{F. Bethuel}, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 7, No. 4, 269--286 (1990; Zbl 0708.58004) Full Text: DOI Numdam EuDML
Bethuel, Fabrice Approximation dans des espaces de Sobolev entre deux variétés et groupes d’homotopie. (Approximation in Sobolev spaces between two manifolds and homotopy groups). (French) Zbl 0651.46040 C. R. Acad. Sci., Paris, Sér. I 307, No. 7, 293-296 (1988). MSC: 46E35 55Q52 PDFBibTeX XMLCite \textit{F. Bethuel}, C. R. Acad. Sci., Paris, Sér. I 307, No. 7, 293--296 (1988; Zbl 0651.46040)