Publications of the Research group for Analysis of Partial Differential Equations

  1. [1]  Simon Eberle. “A heteroclinic orbit connecting traveling waves pertaining to different nonlinearities”. In: Journal of Differential Equations, in press https://doi.org/10.1016/j.jde.2018.03.007 (2018). URL: http://www.sciencedirect. com/science/article/pii/S0022039618301499.

  2. [2]  Simon Eberle. “A heteroclinic orbit connecting traveling waves pertaining to different nonlinearities in a channel with decreasing cross section”. In: Nonlinear Analysis 172 (July 2018), pp. 99–114. URL: https://www.sciencedirect. com/science/article/pii/S0362546X18300567.

  3. [3]  Simon Eberle. Front blocking versus propagation in the presence of drift disturbance in the direction of propagation. 2018. eprint: arXiv:1803.03102.

  4. [4]  Simon Eberle, Barbara Niethammer, and André Schlichting. “Gradient flow formulation and longtime behaviour of a constrained Fokker-Planck equation”. In: Nonlinear Anal. 158 (2017), pp. 142–167. URL: https://doi.org/10. 1016/j.na.2017.04.009.

  5. [5]  Gohar Aleksanyan. “Optimal regularity in the optimal switching problem”. In: Ann. Inst. H. Poincaré Anal. Non Linéaire 33.6 (2016), pp. 1455–1471. URL: https://doi.org/10.1016/j.anihpc.2015.06.001.

  6. [6]  Simon Eberle. “Explicit formulas for homogenization limits in certain non-periodic problems including ramified domains”. In: ZAMM Z. Angew. Math. Mech. 96.10 (2016), pp. 1205–1219. URL: https://doi.org/10.1002/zamm.201500207.

  7. [7]  Mariana Smit Vega Garcia, Eugen Vărv ̆ aruc ̆ a, and Georg S. Weiss. “Singularities in axisymmetric free boundaries for electrohydrodynamic equations”. In: Arch. Ration. Mech. Anal. 222.2 (2016), pp. 573–601. URL: https://doi. org/10.1007/s00205-016-1008-9.

  8. [8]  John Andersson et al. “Equilibrium points of a singular cooperative system with free boundary”. In: Adv. Math. 280 (2015), pp. 743–771. URL: https://doi.org/10.1016/j.aim.2015.04.014.

  9. [9]  Eugen Varvaruca and Georg S. Weiss. “Singularities of steady axisymmetric free surface flows with gravity”. In: Comm. Pure Appl. Math. 67.8 (2014), pp. 1263–1306. URL: https://doi.org/10.1002/cpa.21514.

  10. [10]  John Andersson, Henrik Shahgholian, and Georg S. Weiss. “The singular set of higher dimensional unstable obstacle type problems”. In: Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 24.1 (2013), pp. 123–146. URL: https: //doi.org/10.4171/RLM/648.

  11. [11]  Peter V. Gordon and Georg S. Weiss. “Convective combustion in porous media: singular limit of high activation energy”. In: Nonlinearity 26.1 (2013), pp. 53–63. URL: https://doi.org/10.1088/0951-7715/26/1/53.

  12. [12]  John Andersson, Henrik Shahgholian, and Georg S. Weiss. “Double obstacle problems with obstacles given by non-C2 Hamilton-Jacobi equations”. In: Arch. Ration. Mech. Anal. 206.3 (2012), pp. 779–819. URL: https://doi.org/10. 1007/s00205-012-0541-4.

  13. [13]  John Andersson, Henrik Shahgholian, and Georg S. Weiss. “On the singularities of a free boundary through Fourier expansion”. In: Invent. Math. 187.3 (2012), pp. 535–587. URL: https://doi.org/10.1007/s00222-011-0336-5.

  14. [14]  Sagun Chanillo and Georg S. Weiss. “A remark on the geometry of uniformly rotating stars”. In: J. Differential Equations 253.2 (2012), pp. 553–562. URL: https://doi.org/10.1016/j.jde.2012.04.011.

  15. [15]  Eugen Varvaruca and Georg S. Weiss. “The Stokes conjecture for waves with vorticity”. In: Ann. Inst. H. Poincaré Anal. Non Linéaire 29.6 (2012), pp. 861–885. URL: https://doi.org/10.1016/j.anihpc.2012.05.001.

  16. [16]  Georg S. Weiss and Guanghui Zhang. “A free boundary approach to two-dimensional steady capillary gravity water waves”. In: Arch. Ration. Mech. Anal. 203.3 (2012), pp. 747–768. URL: https://doi.org/10.1007/s00205-011-0466-3.

  17. [17]  Georg S. Weiss and Guanghui Zhang. “The second variation of the stream function energy of water waves with vorticity”. In: J. Differential Equations 253.9 (2012), pp. 2646–2656. URL: https://doi.org/10.1016/j.jde.2012.07.005.

  18. [18]  Eugen Varvaruca and Georg S. Weiss. “A geometric approach to generalized Stokes conjectures”. In: Acta Math. 206.2 (2011), pp. 363–403. URL: https://doi.org/10.1007/s11511-011-0066-y.

  19. [19]  John Andersson, Henrik Shahgholian, and Georg S. Weiss. “Regularity below the C2 threshold for a torsion problem, based on regularity for Hamilton-Jacobi equations”. In: Nonlinear partial differential equations and related topics. Vol. 229. Amer. Math. Soc. Transl. Ser. 2. Amer. Math. Soc., Providence, RI, 2010, pp. 1–14. URL: https: //doi.org/10.1090/trans2/229/01.

  20. [20]  John Andersson, Henrik Shahgholian, and Georg S. Weiss. “Uniform regularity close to cross singularities in an unstable free boundary problem”. In: Comm. Math. Phys. 296.1 (2010), pp. 251–270. URL: https://doi.org/10.1007/s00220- 010-1015-x.

  21. [21]  Georg S. Weiss and Guanghui Zhang. “Existence of a degenerate singularity in the high activation energy limit of a reaction-diffusion equation”. In: Comm. Partial Differential Equations 35.1 (2010), pp. 185–199. URL: https: //doi.org/10.1080/03605300903338322.

  22. [22]  John Andersson and Georg S. Weiss. “A parabolic free boundary problem with Bernoulli type condition on the free boundary”. In: J. Reine Angew. Math. 627 (2009), pp. 213–235. URL: https://doi.org/10.1515/CRELLE.2009.016.

  1. [23]  R. Monneau and G. S. Weiss. “Pulsating traveling waves in the singular limit of a reaction-diffusion system in solid combustion”. In: Ann. Inst. H. Poincaré Anal. Non Linéaire 26.4 (2009), pp. 1207–1222. URL: https://doi.org/10. 1016/j.anihpc.2008.09.002.

  2. [24]  Henrik Shahgholian, Nina Uraltseva, and Georg S. Weiss. “A parabolic two-phase obstacle-like equation”. In: Adv. Math. 221.3 (2009), pp. 861–881. URL: https://doi.org/10.1016/j.aim.2009.01.011.

  3. [25]  R. Monneau and G. S. Weiss. “An unstable elliptic free boundary problem arising in solid combustion”. In: Duke Math. J. 136.2 (2007), pp. 321–341. URL: https://doi.org/10.1215/S0012-7094-07-13624-X.

  4. [26]  R. Monneau and G. S. Weiss. “Self-propagating high temperature synthesis (SHS) in the high activation energy regime”. In: Acta Math. Univ. Comenian. (N.S.) 76.1 (2007), pp. 99–109.

  5. [27]  Henrik Shahgholian, Nina Uraltseva, and Georg S. Weiss. “The two-phase membrane problem—regularity of the free boundaries in higher dimensions”. In: Int. Math. Res. Not. IMRN 8 (2007), Art. ID rnm026, 16. URL: https: //doi.org/10.1093/imrn/rnm026.

  6. [28]  Henrik Shahgholian and Georg S. Weiss. “Aleksandrov and Kelvin reflection and the regularity of free boundaries”. In: Free boundary problems. Vol. 154. Internat. Ser. Numer. Math. Birkhäuser, Basel, 2007, pp. 391–401. URL: https://doi.org/10.1007/978-3-7643-7719-9_38.

  7. [29]  J. Andersson and G. S. Weiss. “Cross-shaped and degenerate singularities in an unstable elliptic free boundary problem”. In: J. Differential Equations 228.2 (2006), pp. 633–640. URL: https://doi.org/10.1016/j.jde.2005.11.008.

  8. [30]  Henrik Shahgholian and Georg S. Weiss. “The two-phase membrane problem—an intersection-comparison approach to the regularity at branch points”. In: Adv. Math. 205.2 (2006), pp. 487–503. URL: https://doi.org/10.1016/j.aim. 2005.07.015.

  9. [31]  Georg S. Weiss. “Regularity in free boundary problems [MR1929893]”. In: Selected papers on differential equations and analysis. Vol. 215. Amer. Math. Soc. Transl. Ser. 2. Amer. Math. Soc., Providence, RI, 2005, pp. 1–13. URL: https://doi.org/10.1090/trans2/215/01.

  10. [32]  Henrik Shahgholian, Nina Uraltseva, and Georg S. Weiss. “Global solutions of an obstacle-problem-like equation with two phases”. In: Monatsh. Math. 142.1-2 (2004), pp. 27–34. URL: https://doi.org/10.1007/s00605-004-0235-6.

  11. [33]  G. S. Weiss. “A parabolic free boundary problem with double pinning”. In: Nonlinear Anal. 57.2 (2004), pp. 153–172. URL: https://doi.org/10.1016/j.na.2004.02.005.

  12. [34]  Georg S. Weiss. “Boundary monotonicity formulae and applications to free boundary problems. I. The elliptic case”. In: Electron. J. Differential Equations (2004), No. 44, 12.

  13. [35]  Hi Jun Choe and Georg Sebastian Weiss. “A semilinear parabolic equation with free boundary”. In: Indiana Univ. Math. J. 52.1 (2003), pp. 19–50. URL: https://doi.org/10.1512/iumj.2003.52.2124.

  14. [36]  G. S. Weiss. “A singular limit arising in combustion theory: fine properties of the free boundary”. In: Calc. Var. Partial Differential Equations 17.3 (2003), pp. 311–340.

  15. [37]  G. S. Weiss. “A singular limit arising in combustion theory: fine properties of the free boundary”. In: Su ̄rikaisekikenkyu ̄sho K ̄oky ̄uroku 1249 (2002). International Conference on Reaction-Diffusion Systems: Theory and Applications (Kyoto, 2001), pp. 126–132.

  16. [38]  Georg S. Weiss. “Regularity in free boundary problems”. In: S ̄ugaku 54.3 (2002), pp. 225–234.

  17. [39]  G. S. Weiss. “A gradient flow approach to a free boundary problem with volume constraint”. In: S ̄urikaisekikenky ̄usho Ko ̄ky ̄uroku 1198 (2001). Numerical solution of partial differential equations and related topics, II (Japanese) (Kyoto, 2000), pp. 117–121.

  18. [40]  G. S. Weiss. “An obstacle-problem-like equation with two phases: pointwise regularity of the solution and an estimate of the Hausdorff dimension of the free boundary”. In: Interfaces Free Bound. 3.2 (2001), pp. 121–128. URL: https://doi.org/10.4171/IFB/35.

  19. [41]  G. S. Weiss. “A singular limit arising in combustion theory: identification of the limit”. In: S ̄urikaisekikenky ̄usho K ̄oky ̄uroku 1178 (2000). Nonlinear diffusive systems—dynamics and asymptotic analysis (Japanese) (Kyoto, 2000), pp. 29–35.

  20. [42]  G. S. Weiss. “The free boundary of a thermal wave in a strongly absorbing medium”. In: J. Differential Equations 160.2 (2000), pp. 357–388. URL: https://doi.org/10.1006/jdeq.1999.3678.

  21. [43]  G. S. Weiss. “A homogeneity improvement approach to the heat equation with strong absorption”. In: Su ̄rikaisekikenkyu ̄sho Ko ̄ky ̄uroku 1076 (1999). Variational problems and related topics (Japanese) (Kyoto, 1998), pp. 133–146.

  22. [44]  G. S. Weiss. “On the two-phase obstacle problem”. In: S ̄urikaisekikenky ̄usho K ̄oky ̄uroku 1117 (1999). Variational problems and related topics (Japanese) (Kyoto, 1999), pp. 134–139.

  23. [45]  G. S. Weiss. “Self-similar blow-up and Hausdorff dimension estimates for a class of parabolic free boundary problems”. In: SIAM J. Math. Anal. 30.3 (1999), pp. 623–644. URL: https://doi.org/10.1137/S0036141097327409.

  1. [46]  Georg S. Weiss. “A homogeneity improvement approach to the obstacle problem”. In: Invent. Math. 138.1 (1999), pp. 23–50. URL: https://doi.org/10.1007/s002220050340.

  2. [47]  Georg Sebastian Weiss. “Partial regularity for a minimum problem with free boundary”. In: J. Geom. Anal. 9.2 (1999), pp. 317–326. URL: https://doi.org/10.1007/BF02921941.

  3. [48]  Georg S. Weiss. “Partial regularity for weak solutions of an elliptic free boundary problem”. In: Comm. Partial Differential Equations 23.3-4 (1998), pp. 439–455. URL: https://doi.org/10.1080/03605309808821352.

  4. [49]  Georg S. Weiss. “Structural properties of a semilinear parabolic equation with free boundary—regularity of singular lines”. In: Proceedings of the International Conference on Asymptotics in Nonlinear Diffusive Systems (Sendai, 1997). Vol. 8. Tohoku Math. Publ. Tohoku Univ., Sendai, 1998, pp. 189–197.

  5. [50]  Georg S. Weiss and Yasumasa Nishiura. “The singular limit of the Cahn-Hilliard equation with a nonlocal term”. In: S ̄urikaisekikenky ̄usho K ̄oky ̄uroku 951 (1996). Variational problems and related topics (Japanese) (Kyoto, 1995), pp. 62–68.

  6. [51]  Georg Sebastian Weiss. “Partial regularity for electrochemical machining with threshold current”. In: Su ̄rikaisekikenkyu ̄sho Ko ̄ky ̄uroku 966 (1996). Nonlinear evolution equations and their applications (Japanese) (Kyoto, 1995), pp. 81–87.

  7. [52]  Georg S. Weiss. “A free boundary problem for non-radial-symmetric quasi-linear elliptic equations”. In: Adv. Math. Sci. Appl. 5.2 (1995), pp. 497–555.

  8. [53]  Georg S. Weiss. “Shape optimization with respect to the boundary condition of elliptic-parabolic systems”. In: Adv. Math. Sci. Appl. 5.2 (1995), pp. 717–741.