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Workgroup Nonlinear Partial Differential Equations

Secretariat
Kollegiengebäude Mathematik (20.30)
Room 3.029

Address
Karlsruher Institut für Technologie
Institut für Analysis
Englerstraße 2
76131 Karlsruhe
Germany

Office hours:
Mon-Fri 10-12, Tue+Thu 14-16

Tel.: +49 721 608 42064

Fax.: +49 721 608 46530

Publications

Publications and papers:

43. Ground states of a nonlinear curl-curl problem in cylindrically symmetric media. Joint work with Th. Bartsch (Univ. Giessen), T. Dohnal (Univ. Dortmund), M. Plum (KIT). NoDEA Nonlinear Differential Equations Appl. 23 (2016), no. 5, Art. 52, 34 pp.

42. Mesh-independent a priori bounds for nonlinear elliptic finite difference boundary value problems. Joint work with P.J. McKenna (Univ. Connecticut) and A. Verbitsky (KIT). J. Math. Anal. Appl. 419 (2014), no. 1, 496–524.

41. Distributional solutions of the stationary nonlinear Schrödinger equation: singularities, regularity and exponential decay. Joint work with R. Mandel (KIT). Z. Anal. Anwend. 32 (2013), no. 1, 55–82.

40. Interfaces supporting surface gap soliton ground states in the 1D nonlinear Schrödinger equation. Joint work with T. Dohnal (Univ. Dortmund), K. Nagatou (KIT) and M. Plum (KIT). J. Math. Anal. Appl. 407 (2013), no. 2, 425–435.

39. Symmetry of solutions for quasimonotone second-order elliptic systems in ordered Banach spaces. Joint work with G. Herzog (KIT). Math. Ann. 352 (2012), 99--112.

38. Surface gap soliton ground states for the nonlinear Schrödinger equation. Joint work with T. Dohnal (Univ. Dortmund) and M. Plum (KIT). Comm. Math. Phys. 308 (2011), 511--542.

37. In memoriam Wolfgang Walter (1927–2010). (German) Jahresber. Dtsch. Math.-Ver. 113 (2011), no. 2, 57–79.

36. Large solutions to semilinear elliptic equations with Hardy potential and exponential nonlinearity. Joint work with C. Bandle (Basel) and V. Moroz (Swansea). Around the research of Vladimir Maz'ya. II, 1-22, Int. Math. Ser. (N.Y.), 12, Springer, New York, 2010.

35. Existence of solutions to nonlinear, subcritical higher-order elliptic Dirichlet problems. Joint work with T. Weth (Univ. Giessen). J. Differential Equations 248 (2010), No. 7, 1866-1878.

34. Localized modes of the linear periodic Schrödinger operator with a nonlocal perturbation. Joint work with T. Dohnal and M. Plum (Univ. Karlsruhe). SIAM J. Math. Anal., Volume 41, Issue 5 (2009), 1967--1993.

33. Characterization of balls by Riesz-potentials. Ann. Mat. Pura Appl. 188 (2009), 235--245.

32. Very weak solutions with boundary singularities for semilinear elliptic Dirichlet problems in domains with conical corners. Joint work with J. Horák (Univ. zu Köln) and P.J. McKenna (Univ. Connecticut). J. Math. Anal. Appl. 352 (2009), 496 -- 514.

31. A priori bounds and a Liouville theorem on a half-space for higher-order elliptic Dirichlet problems. Joint work with T. Weth (Univ. Giessen). Math. Z. 261 (2009), 805--827.

30. The Paneitz equation in hyperbolic space. Joint work with H.-Ch. Grunau (Univ. Magdeburg) and M. Ould Ahmedou
(Univ. Tübingen). Ann. Inst. H. Poincaré (C) Anal. Non Linéaire . 25 (2008), 847 -- 864.

29. Very weak solutions to elliptic problems with nonlinear Neumann boundary conditions. Joint work with P. Quittner (Univ. Bratislava). Calc. Var. Partial Differential Equations 32 (2008), 429--452.

28. \"Boundary blowup\" type sub-solutions to semilinear elliptic equations with Hardy potential. Joint work with C. Bandle (Univ. Basel) and V. Moroz (Univ. Bristol). J. London Math. Soc. 77 (2008), 503--523.

27. Positivity and anti-maximum principles for elliptic operators with mixed boundary conditions. Joint work with C. Bandle (Univ. Basel) and J. von Below (Univ. Littoral Côte d'Opal). J. Eur. Math. Soc. 10 (2008), 73--104.

26. Gidas-Ni-Nirenberg results for finite difference equations: Estimates of approximate symmetry. Joint work with P.J. McKenna (Univ. of Connecticut). J. Math. Anal. Appl. 3354 (2007), 206--222.

25. A priori bounds for semilinear elliptic equations and a new class of critical exponents for Lipschitz domains. Joint work with P.J. McKenna (Univ. Connecticut). J. Funct. Anal. 244 (2007), 220--246.

24. Parabolic problems with dynamical boundary conditions: eigenvalue expansions and blow up. Joint work with C. Bandle (Univ. Basel) and J. von Below (Univ. Littoral Côte d'Opale). Rend. Lincei Mat. Appl. 17 (2006), 35--67.

23. Global solution branches for p-Laplacian boundary value problems. Joint work with J. Fleckinger (Univ. Toulouse). Nonlinear Analysis T.M.A. 62 (2005), 53--70.

22. Eigenvalues of the radially symmetric p-Laplacian in IR^n. Joint work with B.M. Brown (Univ. Cardiff). J. London Math. Soc. 69 (2004), 657--675.

21. Analytical and numerical results for the Fucik spectrum of the Laplacian. Joint work with J. Horák (Univ. Basel). J. Comput. Appl. Math. 161 (2003), 313--338.

20. Uniqueness results for semilinear polyharmonic boundary value problems on conformally contractible domains: Part (II). J. Math. Anal. Appl. 287 (2003), 75--89.

19. Uniqueness results for semilinear polyharmonic boundary value problems on conformally contractible domains: Part (I). J. Math. Anal. Appl. 287 (2003), 61--74.

18. Sharp parameter ranges in the uniform anti-maximum principle for second-order ordinary differential operators. Z. angew. Math. Phys. 54 (2003), 822--838.

17. Positive solutions of linear elliptic equations with critical growth in the Neumann boundary condition. Joint work with M. Chlebik and M. Fila (Univ. Bratislava). NoDeA 10 (2003), 329--346.

16. Radial solutions of singular nonlinear biharmonic equations and applications to conformal geometry. Joint work with P.J. McKenna (Univ. Connecticut). Electronic J. Diff. Eqns. 2003 (2003), No. 37, 1--13.

15. Computing eigenvalues and Fucik-spectrum of the radially-symmetric p-Laplacian. Joint work with M. Brown (Univ. Cardiff). J. Comput. Appl. Math. 148 (2002), 183--211.

14. Existence and starshapedness for the Lane-Emden equation. Joint work with A. Greco (Univ. Cagliari). Applicable Analysis 78 (2001), 21--32.

13. Sign-changing solutions to singular second-order boundary value problems. Joint work with P.J. McKenna (Univ. Connecticut). Advances in Differential Equations 6 (2001), 441-460.

12. Electrostatic characterization of spheres. Joint work with O. Mendez (Univ. Missouri). Forum Mathematicum 12 (2000), 223--245.

11. Non-existence results for semilinear cooperative elliptic systems via moving spheres. Joint work with Henghui Zou (Univ. Alabama). J. Differential Equations 161 (2000), 219--243.

10. Existence and uniqueness theorems for singular anisotropic quasilinear elliptic boundary value problems. Joint work with S. Hill and K.S. Moore (Univ. of Connecticut). Proceedings Amer. Math. Soc. 128 (2000), 1673--1683.

9. Approximate radial symmetry for overdetermined boundary value problems. Joint work with A. Aftalion and J. Busca (Ecole Norm. Sup. Paris). Advances in Differential Equations 4 (1999), 907--932.

8. Sturm-Liouville type problems for the p-Laplacian under asymptotic non-resonance conditions. Joint work with W. Walter (Univ. Karlsruhe). J. Differential Equations 156 (1999), 50--70.

7. Existence of two boundary blow-up solutions for semilinear elliptic equations. Joint work with A. Aftalion (Ecole Norm. Sup. Paris). J. Differential Equations 141 (1997), 400--421.

6. Radial solutions of equations and inequalities involving the p-Laplacian. Joint work with W. Walter (Univ. Karlsruhe). J. Inequal. & Appl. 1 (1997), 47--71.

5. Radial symmetry for an electrostatic and a capillarity problem. ZAMM 77 (1997) S2, S653--S654.

4. Uniqueness for degenerate elliptic equations via Serrin's sweeping principle. Intern. Series of Num. Math. 123 (1997), 375--387.

3. Symmetry and multiplicity for nonlinear elliptic differential equations with boundary blow-up. Joint work with
W. Walter (Univ. Karlsruhe), P.J. McKenna (Univ. Connecticut). Nonlinear Analysis T.M.A. 28 (1997), 1213--1225.

2. Radial symmetry for elliptic boundary value problems on exterior domains. Arch. Rational Mech. Anal. 137 (1997), 381--394.

1. Radial symmetry for an electrostatic, a capillarity and some fully nonlinear overdetermined problems on exterior domains. Z. für Analysis und ihre Anwendungen 15 (1996), 619--635.


Preprints, submitted papers:

1. A priori bounds and global bifurcation results for frequency combs modeled by the Lugiato-Lefever equation. Joint work with R. Mandel (KIT). Accepted in SIAM J. Appl. Math.

2. Existence of cylindrically symmetric ground states to a nonlinear curl-curl equation with non-constant coefficients. Joint work with A. Hirsch (KIT). arXiv:1606.04415.

3. A breather construction for a semilinear curl-curl wave equation with radially symmetric coefficients. Joint work with M.Plum (KIT). arXiv:1610.09203


Monographs and contributions to books:


1. Uniqueness theorems for variational problems by the method of transformation groups. Springer Lecture Notes in Mathematics, Vol. 1841, 152 pp., ISBN: 3-540-21839-4, 2004.

2. Solutions of quasilinear second order elliptic boundary value problems via degree theory. Joint work with C. Bandle (Basel). pp. 1--70, Handbook of Differential Equations: Stationary Partial Differential Equations, Volume 1, Elsevier, North Holland, ISBN: 0-444-51126-1, 2004.



Contributions to conference proceedings:


1. Radial symmetry by moving planes for semilinear elliptic boundary value problems on annuli and other non-convex domains. Progress in Partial Differential Equations: Elliptic and Parabolic Problems, Ed. C. Bandle et al., Pitman Res. Notes 325 (1995), 164--182.

2. Supercritical variational problems with unique critical points. Proceedings of the 4th European Conference on Elliptic and Parabolic Problems, Rolduc, June 2001. World Scientific (2002), 253--262.

3. A linear parabolic problem with non-dissipative dynamical boundary conditions. Joint work with C. Bandle (Univ. Basel). Proceedings of the Swiss-Japanese Seminar on Elliptic and Parabolic Problems, Zürich, 2004. Eds. M. Chipot, H. Ninomiya, World Scientific, 2005.



Theses:


Master thesis:
Variational methods in bifurcation theory for non-Fredholm problems, (1992). Advisor: Prof. John Toland
(Univ. of Bath)

Diplom thesis:
Symmetry of solutions of semilinear elliptic differential equations, (1993). Advisor: Prof. Dr. P. Volkmann (Univ. Karlsruhe)

Doctoral thesis:
Large solutions and overdetermined boundary value problems for quasilinear elliptic differential
equations, (1996). Referees: Prof. Dr. W. Walter (Univ. Karlsruhe), Prof. Dr. C. Bandle (Univ. Basel).

Habilitation thesis:
Uniqueness theorems for variational problems by the method of transformation groups, (2002),
Universität Basel.