Publications of Michael Struwe

Publications



Monographs

  • Plateau's problem and the Calculus of Variations, Math. Notes 35, Princeton University Press (1989).
  • Variational methods, Springer (1990); second edition: Ergebnisse Math. 34, Springer (1996); third edition (2000); fourth edition (2008).
  • (with J. Shatah) Geometric wave equations, Courant Lect. Notes 2 (1998), Courant Institute, New York; second edition, AMS (2000).


    • Selected Research Publications and Surveys

  • Infinitely many critical points for functionals which are not even and applications to superlinear boundary value problems, manusc. math. 32, 335-364 (1980).
  • (with M. Giaquinta) An optimal regularity result for quasilinear parabolic systems, manusc. math. 36, 223-239 (1981).
  • Multiple solutions of differential equations without the Palais-Smale condition, Math. Ann. 261, 399-412 (1982).
  • Nonuniqueness in the Plateau problem for surfaces of constant mean curvature, Arch. Rat. Mech. Anal. 93, 135-157 (1986), submitted to ARMA on August 13, 1982.
  • On a critical point theory for minimal surfaces spanning a wire in {\Bbb R}^n, J. Reine Angewandte Math. 349, 1-23 (1984).
  • On a free boundary problem for minimal surfaces, Inventiones Math. 75, 547-560 (1984).
  • A global compactness result for elliptic boundary value problems involving limiting nonlinearities, Math. Z. 187, 511-517 (1984).
  • On the evolution of harmonic mappings of Riemannian surfaces, Comm. Math. Helv. 60, 558-581 (1985).
  • The existence of surfaces of constant mean curvature with free boundaries, Acta Math. 160, 19-64 (1988).
  • Partial regularity results for the Navier-Stokes-equations, Comm. Pure Appl. Math. XLI, 437-458 (1988).
  • The evolution of harmonic maps in higher dimensions, J. Differential Geometry 28 (1988), 485-502.
  • Globally regular solutions to the $u^5$-Klein-Gordon equations, Annali Sc. Norm. Sup. Pisa (Ser. 4) 15 (1988), 495-513.
  • (with Y. Chen) Existence and partial regularity results for the heat flow for harmonic maps, Math. Z. 201 (1989), 83-103.
  • (with J. Jost) Morse-Conley theory for minimal surfaces of varying topological type, Invent. Math. 102 (1990), 465-499.
  • (with A. Ambrosetti) The existence of steady vortex rings in an ideal fluid, Arch. Rat. Mech. Anal. 108 (1989), 97-109.
  • Existence of periodic solutions of Hamiltonian systems on almost every energy surface, Boletim Soc. Bras. Mat. 20 (1990), 49-58.
  • Semi-linear wave equations, Bull. Amer. Math. Soc. 26.1 (1992), 53--85.
  • (with J. Fr\"ohlich) Variational problems on vector bundles, Comm. Math. Phys. 131 (1990), 431-464.
  • The evolution of harmonic maps, Proc. Intern. Congress Math. Kyoto 1990, 1197-1203, Springer-Verlag, Tokyo (1991).
  • (with J. Moser) On a Liouville-type theorem for linear and nonlinear elliptic differential equations on a torus, Bol. Soc. Bras. Mat. 23 (1992), 1-20.
  • (with J. Shatah) Regularity results for nonlinear wave equations, Annals of Math. 138 (1993), 503--518.
  • Geometric evolution problems, in: Nonlinear PDE in differential geometry (eds.: R. Hardt, M. Wolf), Proceedings of 1992 graduate summer school, IAS/Park City Math.~Ser.~2 (1996), 259--339.
  • Das Plateausche Problem, Jahresbericht Dt.~Math.-Ver.~96 (1994), 101--116.
  • (with J.~Bartz and R.~Je) A new approach to the Ricci flow on $S^2$; Annali Sc.~Norm.~Sup.~Pisa (Ser.~IV) 21 (1994), 475--482.
  • The Yang-Mills flow in four dimensions, Cal.~Var.~2 (1994), 123--150.
  • Une estimation asymptotique pour le mod\`ele Ginzburg-Landau, C.~R.~Acad. Sci. Paris, 317, S\'er.~1 (1993), 677--680.
  • On the asymptotic behavior of minimizers of the Ginzburg-Landau model in 2 dimensions. Differential and Integral Equations, 7 (1994), 1613-1624.
  • Regular Solutions of the stationary Navier-Stokes equations on {\Bbb R}^5, Mathematische Annalen 302 (1995), 719-741.
  • (with J. Shatah) Well-posedness in the energy space for semi-linear wave equations with critical growth, IMRN 1994, No.7, 303-309.
  • Singular perturbations of geometric variational problems, in: Elliptic and Parabolic Methods in Geometry (eds.: B. Chow et al.), A.K. Peters, Wellesley, Ma., (1995), 123-144.
  • Sattelpunkte oder Variationsprinzipien in Geometrie und Mechanik, Elemente Math. 52 (1997), 45-59.
  • Evolution problems in geometry and mathematical physics, in: Prospects in Mathematics, Invited talks on the occasion of the 250th anniversary of Princeton University 1996 (ed.: H. Rossi), Amer. Math. Soc. (1999), 83-101.
  • (with M.-C. Hong and J. Jost), Asymptotic limits of a Ginzburg-Landau type functional, in: Geometric analysis and the calculus of variations (ed. J. Jost), International Press (1996), 99-123; preprint (1996) .
  • Wave maps, in: Nonlinear Differential Equations in Geometry and Physics, 1995 Barrett lectures (eds.: G. Baker, A. Freire), PNLDE 29, Birkhäuser (1997), 113-153; preprint (1996) .
  • (with A. Freire and S. Müller) Weak convergence of wave maps from (1+2)-dimensional Minkowski space to Riemannian manifolds, Inventiones Math. 130 (1997), 589-617.
  • (with A. Freire and S. Müller) Weak compactness of wave maps and harmonic maps, Ann. Inst. H. Poincari, Analyse Non-Linéaire 15.6 (1998), 725-754.
  • (with S. Müller) Global existence of wave maps in 1+2 dimensions with finite energy data, Topological methods in nonlinear analysis 7 (1996), 245-259, preprint (1996) .
  • (with A. Schlatter and A. Shadi Tahvildar-Zadeh) Global existence of the equivariant Yang-Mills flow in four dimensions, Amer. J. Math. 120 (1998), 117-128. (In the publication process, the paper was inadvertently changed by the printer. The authorized version of the paper can be found in the online version of the journal, only. The 1996 preprint, which is almost identical to the corrected online version, can be downloaded here.)
  • (with G. Tarantello) On multivortex solutions in Chern-Simons gauge theory, Boll. UMI (8) 1-B (1998), 109-121.
  • (with S. Müller and V. Sverak) Harmonic maps on planar lattices, Annali Sc. Norm. Sup. Pisa Cl. Sci., Ser. IV, 25 (1997), 713-730.
  • Uniqueness of harmonic maps with small energy, manusc. math. 96 (1998), 463-486.
  • (with S. Müller) Spatially discrete wave maps on (1 + 2)-dimensional space-time, Top. Meth. Nonlin. Analysis 11 (1998), 295-320, preprint (1998) .
  • (with C. Imbusch) Variational principles for minimal surfaces, in: Topics in nonlinear analysis, (eds.: J.~Escher, G.~Simonett), Progr. Nonlin. Diff. Eqs. Appl. 35, Birkh\"auser (1999), 477-498, preprint (1997) .
  • Uniqueness for critical nonlinear wave equations and wave maps via the energy inequality, Comm. Pure Appl. Math. 52 (1999), 1179-1188.
  • (with Adimurthi) Global compactness properties of semilinear elliptic equations with critical exponential growth, J.~Funct.~Analysis 175 (2000), 125-167; see online link .
  • Positive solutions of critical semilinear elliptic equations on non-contractible planar domains, J.~European Math.~Soc. 2 (2000), 329-388; see online link .
  • Curvature flows on surfaces, Annali Sc. Norm. Sup. Pisa Serie V, 1 (2002), 247-274 ( preprint (2000)).
  • Equivariant wave maps in two space dimensions, Comm. Pure Appl. Math. 56 (2003), 815-823, preprint (2000) .
  • Radially symmetric wave maps from (1 + 2)-dimensional Minkowski space to the sphere, Math. Z. 242 (2002), 407-414; see online link .
  • (with Jalal Shatah) The Cauchy problem for wave maps, IMRN 2002, No.11, 555-571; see online link .
  • Radially symmetric wave maps from (1 + 2)-dimensional Minkowski space to general targets, Calculus of Variations 16 (2003), 431-437; see online link .
  • (with H.~Schwetlick) Convergence of the Yamabe flow for "large" energies, J. Reine Angew. Math. 562 (2003), 59-100, preprint (2002).
  • Olga Ladyshenskaya - A life-long devotion to mathematics, Laudatio, May 13, 2002; in: ``Geometric Analysis and Nonlinear Partial Differential Equations'', Abschlussbericht des SFB 256, Univ. Bonn, (Editors: S. Hildebrandt und H. Karcher), Springer Verlag, 2003, ISBN: 3-540-44051-8, pp. 1-10; see: www.springeronline.com/3-540-44051-8.
  • (with N. Hungerb\"uhler) A one-way function from thermodynamics and applications to cryptography, Elemente Math. 58 (2003), 49-64, preprint (2002).
  • (with F. Robert) Asymptotic profile for a fourth order PDE with critical exponential growth in dimension four, Advanced Nonlinear Studies 4 (2004), 397-415, preprint (2003).
  • A flow approach to Nirenberg's problem, Duke Mathematical Journal 128 (2005), 19-64, preprint (2004).
  • (with A. Malchiodi) Q-curvature flow on $S^4$, Journal of Differential Geometry 73 (2006), 1-44, preprint (2004) .
  • (with Adimurthi and F. Robert) Concentration phenomena for Liouville's equation in dimension 4, Journal European Math. Soc. 8 (2006), 171-180, preprint (2005) .
  • On a Serrin-type regularity criterion for the Navier-Stokes equations in terms of the pressure, Journal Math. Fluid Mechanics 9 (2007), 235-242; see online link or preprint (2005) .
  • On uniqueness and stability for supercritical nonlinear wave and Schrödinger equations, IMRN 2006, Article ID 76737, 1-14, preprint (2005) .
  • Quantization for a fourth order equation with critical exponential growth, Math. Z. 256 (2007), 397-424; see online link or preprint (2006).
  • (with Tristan Rivière) Partial regularity for harmonic maps, and related problems, Comm. Pure Applied Mathematics 61 (2008), 451-463, preprint (2006).
  • Partial regularity for biharmonic maps, revisited, Calculus of Variations 33 (2008), 249-262; see online link or preprint (2007).
  • (with Tobias Lamm and Fréderic Robert) The heat flow with a critical exponential nonlinearity, Journal of Functional Analysis 257 (2009), 2951-2998; see online link or preprint (2009).
  • Global well-posedness of the Cauchy problem for a super-critical nonlinear wave equation in 2 space dimensions, Math. Annalen 350 (2011), 707-719; see online link or preprint (2010).
  • (with Luca Martinazzi) Quantization for an elliptic equation of order 2m with critical exponential non-linearity, Math. Zeitschrift 270.1 (2012), 453-486; see online link or preprint (2010).
  • The critical nonlinear wave equation in 2 space dimensions, J. European Math. Soc. 15 (2013), 1805-1823; see online link or preprint (2010).
  • A super-critical nonlinear wave equation in 2 space dimensions, Milan Journal of Mathematics 79.1 (2011), 129-143; see online link or Springer online link.
  • (with Franziska Borer and Luca Galimberti) "Large" conformal metrics of prescribed Gauss curvature on surfaces of higher genus, Comment. Math. Helv. 90 (2015), no. 2, 407-428; see online link or preprint (2013) (update of our previous preprint "Prescribed Gauss curvature on closed surfaces of higher genus").
  • Wave maps with and without symmetries, in "Evolution Equations", (eds. David Ellwood, Igor Rodnianski, and Gigliola Staffilani), Clay Mathematics Proceedings 17, Amer. Math. Soc. (2013), 483-510; preprint (2008).
  • (with Melanie Rupflin) Supercritical elliptic equations, Advanced Nonlinear Studies 12 (2012), 877-887; preprint (2012). Addendum, Advanced Nonlinear Studies 13 (2013), 795-797; preprint (2013).
  • (with Simon Blatt) An analytic framework for the supercritical Lane-Emden equation and its gradient flow, International Mathematics Research Notices (IMRN) 2014; see online link or preprint (2013).
  • The supercritical Lane-Emden equation and its gradient flow, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 25 (2014), no. 4, 359-367; see online link or preprint (2013).
  • (with Martin Sack) Scattering for a critical nonlinear wave equation in two space dimensions, Mathematische Annalen, 365 (2016), no. 3, 969-985; see online link or preprint (2014).
  • (with Simon Blatt) Boundary regularity for the supercritical Lane-Emden heat flow, Calc. Var. 54 (2015), no. 2, 2269-2284; see online link or preprint (2014). In the published version a formula was inadvertently changed by the publisher. The correct formula is given in the Publisher's erratum, Calc. Var. 54 (2015), 2285; see online link.
  • (with Simon Blatt) Well-posedness of the supercritical Lane-Emden heat flow in Morrey spaces, ESAIM: Control, Optimisation and Calculus of Variations (2016) online link, preprint (2015).
  • Variational Methods in Geometry, Jahresbericht der Deutschen Mathematiker-Vereinigung (to appear), DOI: 10.1365/s13291-016-0155-0, online link.
  • Review of the book by D.-A. Geba, M. G. Grillakis: "An Introduction to the Theory of Wave Maps and Related Geometric Problems", Jahresbericht der Deutschen Mathematiker-Vereinigung (to appear), DOI: 10.1365/s13291-017-0166-5, online link,
  • "Bubbling" of the prescribed curvature flow on the torus, J.~Europ.~Math.~Soc. (JEMS) 22.10 (2020), 3223–3262; see online link, or preprint (2017).
  • Normalized harmonic map heat flow, Communications on Pure and Applied Mathematics 73.3 (2020), 664-686; see online link, or preprint (2018).
  • A Liouville-type result for a fourth order equation in conformal geometry, Vietnam Journal of Mathematics 49.2 (2021), 267-279; see online link, or preprint (2019).
  • Plateau flow or the heat flow for half-harmonic maps, Analysis & PDE 17.4 (2024), 1397-1438; see online link, or preprint (2022).
  • “Bubbling” and Topological Degeneration in the Calculus of Variations, Milan Journal of Mathematics (2023); see online link.
  • The prescribed curvature flow on the disc; see preprint (2024) .