Research Interests
Partial differential equations, real harmonic analysis, dispersive equations, fluid dynamics.


Publications
  1. H. Koch, H. F. Smith and D. Tataru. Sharp Lq bounds on spectral clusters for Hölder metrics. (2006) Mathematical Research Letters, to appear.
  2. H. Koch and J.-C. Saut. Local smoothing and local solvability for third order dispersive equations. (2006) SIAM J. Math. Analysis, to appear. Article.
  3. H. Koch and N. Tzvetkov. On finite energy solutions of the KP-I equation. (2006) arXiv:math.AP/0603746.
  4. H. Koch, D. Tataru and M. Zworski. Semiclassical Lp estimates. (2006) Annales Henri Poincaré, to appear. arXiv:math-ph/0603080.
  5. J. Kato and H. Koch. Uniqueness of the modified Schrödinger map in H^{3/4+e}(R^2). (2005) Comm. PDE, to appear. arXiv:math.AP/0508423.
  6. H. Koch and D. Tataru. Carleman estimates and absence of embedded eigenvalues. (2005) Comm. Math. Pys., to appear. arXiv:math-ph/0508052.
  7. H. Koch, G. Leoni and M. Morini. On optimal regularity of free boundary problems and a conjecture of De Giorgi. Commun. Pure Appl. Math 58, No 8, 1051-1076 (2005).
  8. H. Koch and D. Tataru. Dispersive estimates for principally normal pseudodifferential operators. Commun. Pure Appl. Math. 58, No 2, 217-284 (2005).
  9. H. Koch and D. Tataru. Lp eigenfunction bounds for the Hermite operator. Duke Math. J. 128, No 2, 369-392 (2005).
  10. H. Koch and F. Ricci. Spectral projections for the twisted Lacplacian. (2004) Studia Math, to appear. arXiv:math.AP/0412236.
  11. H. Koch and N. Tzvetkov. Nonlinear wave interactions for the Benjamin-Ono equation. Int. Math. Res. Not. 2005, No 30, 1833-1847 (2005)
  12. H. Koch and D. Tataru. Lp eigenfunction bounds for the Hermite operator. (2004) arXiv:math.AP/0402261.
  13. S. Benachour, H. Koch and P. Laurencot. Very singular solutions to a nonlinear parabolic equation with absorption. II: Uniqueness. Proc. R. Soc. Edinb., Sect. A, Math. 134, No 1, 39-54 (2004).
  14. H. Koch. Partial differential equations and singular integrals. Dispersive nonlinear problems in mathematical physics, 59-122, Quad. Mat., 15, Dept. Math., Seconda Univ. Napoli, Caserta (2004).
  15. M. Ben-Artzi, H. Koch and J.-C. Saut. Dispersion estimates for third order equations in two dimensions. Commun. Partial Differ. Equations 28, No 11-12, 1943-1974 (2003).
  16. H. Koch and D. Tataru. Dispersive estimates for principally normal operators and applications to unique continuation. F. Colombini (ed.) et al., Hyperbolic problems and related topics. Proceedings of the conference, Cortona, Italy, September 10-14,2002. Somerville, MA: International Press. Grad. Ser. Anal., 201-217 (2003).
  17. H. Koch and V. A. Solonnikov. Lq-estimates of the first-order derivatives of solutions to the nonstationary Stokes problem. M. Sh. Birman (ed.) et al., Nonlinear problems in mathematical physics and related topics I. In honor of Professor O. A. Ladyzhenskaya. New York, NY: Kluwer Academic/Plenum Publishers. Int. Math. Ser., N.Y. 1, 203-218 (2002).
  18. H. Koch and I. Lasiecka. Hadamard well-posedness of weak solutions in nonlinear dynamic elasticity-full von Karman systems. A. Lorenzi (ed.) et al., Evolution equations, semigroups and functional analysis. In memory of B. Terreni. Containing papers of the conference, Milano, Italy, September 27-28, 2000. Basel: Birkhäuser. Prog. Nonlinear Differ. Equ. Appl. 50, 197-216 (2002).
  19. H. Koch and V. A. Solonnikov. Lq-Estimates for a solutions to the nonstationary Stokes equation. Function theory and phase trasnitions. J. Math. Sci. (New York)106, No 3, 3042-3072 (2001).
  20. H. Koch and D. Tataru: Recent results on unique continuation for second order elliptic equations. F. Colombini (ed.) et al., Carleman estimates and applications to uniqueness and control theory. Boston, Ma: Birkhäuser. Prog. Nonlinear Differ. Equ. Appl. 46, 73-84 (2001).
  21. H. Koch and W. Sickel: Pointwise multipliers of Besov spaces of smoothness zero and spaces of continuous functions. Rev. Mat. Iberoam. 18, No 3, 587-626 (2002).
  22. H. Koch and D. Tataru: Sharp counterexamples in unique countinuation for second order elliptic equations. J. Reine Angew. Math. 542, 133-146 (2002).
  23. H. Koch and D. Tataru: Carleman estimates and unique continuation for second-order elliptic equations with nonsmooth coefficients. Commun. Pure Appl. Math. 54, No 3, 339-360 (2001). CPAM.
  24. M. Ben-Artzi, J.-C. Saut and H. Koch: Dispersion estimates for fourth order Schrödinger equations. C.R. Acad. Sci. Paris, Serie I, Math. 330, No 2, 87-92, 2000. CMP 1 770 930
  25. H. Koch and D. Tataru: Well-posedness for the Navier-Stokes equations. Advances in Math. 157, No 1, 22-35, 2001 . Article.
  26. H. Koch: Transport and instability for perfect fluids. Math. Ann. 323, No 3, 491-523 (2002).
  27. H. Koch: Instability for incompressible and inviscid fluids. W. Jäger. (ed.) et al., Partial differential equations: theory and numerical solution. Proceedings of the ICM'98 satellite conference, Prague, Czech Republic, August 10-16, 1998. Boca Raton, FL: Chapman & Hall/CRC. Chapman Hall/CRC Res. Notes Math. 406, 240-247 (2000).
  28. H. Koch: Non-Euclidean singular integrals and the porous medium equation. Habilitation thesis 1999. (500k)
  29. M. Ben-Artzi and H. Koch: Decay of mass for a semilinear parabolic equation. Commun. Partial Differ. Equations, 24, No 5-6, 869-881, (1999). MR 2000a:35098
  30. C. Kenig, H. Koch, J. Pipher and T. Toro: A new approach to absolute continuity of elliptic measure, with applications to non-symmetric equations. Adv. Math. 153, No 2, 231-298 (2000).
  31. H. Koch: Differentiability of parabolic semi-flows in Lp-spaces and inertial manifolds J. Dyn. Diff. Equations 12, No 3, 511-531 (2000). Article
  32. S. S. Antman and H. Koch: Self-sustained oscillations of nonlinearly viscoelastic layers. SIAM J. Appl. Math. 60, No 4, 1357-1387 (2000). CMP 1 760 039
  33. H. Koch and S. S. Antman: Stability and Hopf bifurcation for fully nonlinear parabolic-hyperbolic equations. SIAM J. Math. Anal. 32, No 2, 360-384 (2000).
  34. H. Koch: Slow decay in linear thermoelasticity. Quarterly Appl. Math., 58, No 4, 601-612 (2000). SFB359 Preprint 1997-17 (101k), , MR 2002a:74043
  35. H. Koch: Classical solutions to phase transition problems are smooth. Commun. Partial Differ. Equations 23, No 3-4, 389-437 (1998). MR 99g:35146
  36. U. Bunke, H. Koch: The Etaform and a generalized Maslov index. Manuscripta Math.95, No 2, 189-212 (1998). MR 99b:58221
  37. H. Koch: On center manifolds. Nonlinear Anal., Theory Methods Appl. 28, No 7, 1227-1248 (1997). MR 99m:34097
  38. H. Koch: Finite dimensional aspects of semilinear parabolic equations. J. Dynamics Diff. Equations 8, No 2, 177-202 (1996).
  39. H. Koch: Global classical solutions to a two phase Stefan problem. M. Demuth (ed.) et al., Differential equations, asymptotic analysis, and mathematical physics. Papers associated with the international conference on partial differential equations, Potsdam, Germany, June 29-July2, 1996. Akademie Verlag Math. Res 100, 181-183 (1997). CMP 1 456 189
  40. H. Koch: On a fully nonlinear mixed parabolic problem with oblique boundary condition. Preprint, SFB 359, Heidelberg, 1995.
  41. J. Cooper and H. Koch: Remarks on the spectrum of a linear wave operator with time periodic boundary condition. A. C. McBride (ed.) et al., Recent developments in evolution equations. Proceedings of a meeting held at the University of Strathclyde, UK, 25-29 July, 1994. Harlow: Longman Scientific & Technical. Pitman Res. Notes Math. Ser. 324, 94-99 (1995).
  42. J. Cooper and H. Koch: The spectrum of a hyperbolic evolution operator. J. Funct. Anal., 133, No 2, 301-328,(1995).
  43. H. Koch and D. Tataru: On the spectrum of hyperbolic semigroups. Commun. Partial Differential Equations, 20, No 5-6, 901-937 (1995).
  44. H. Koch and A. Stahel: Global existence of classical solutions to the dynamical von Karman equations. Math. Methods Appl. Sci. 16, No 8, 581-586 (1993).
  45. H. Koch: Small periodic solutions to quasilinear hyperbolic equations. C. Perello (ed.) et al., International conference on differential equations. Vol. 1, 2. Proceedings of the conference, EQUADIFF 91, Bercelona, Spain, August 26-31 (1991).
  46. H. Koch: Mixed problems for fully nonlinear hyperbolic equations. Math. Z., 214, No 1, 9-42 (1993).
  47. H. Koch: Hyperbolic equations of second order. Heidelberg: Univ. Heidelberg, Naturwiss.-Math. Fak., Thesis. 104p. (1990).


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