Free Boundary Problems and Monotonicity Formulas

2008 Fiscal Year Final Research Report

• Project/Area Number: 18740086
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Global analysis
• Research Institution: The University of Tokyo
• Principal Investigator: WEISS Georg Sebastian The University of Tokyo, 数理科学研究科, 准教授 (30282817)
• Project Period (FY): 2006 – 2008
• Keywords: 非線形偏微分方程式 / 自由境界問題 / 固体燃焼理論 / パターン形成 / 特異点

Research Abstract

個体燃焼理論等に現れる現代的自由境界問題の現象を研究し、その解析に役立つ新しい方法を示した。

Research Products

• [Journal Article] A parabolic obstacle-problem-like equation (2009)
  • Author(s): Henrik Shahgholian, Nina Uraltseva, Georg S. Weiss
  • Journal Title: Adv. Math. 221 Pages: 861-881
  • Peer Reviewed
• [Journal Article] Pulsating traveling waves in the singular limit of a reaction-diffusion system in solid combustion (2009)
  • Author(s): egis Monneau, Georg S. Weiss
  • Journal Title: Annales de l'Institut Henri Poincare
  • Peer Reviewed
• [Journal Article] A parabolic free boundary problem with Bernoulli type condition on the free boundary (2009)
  • Author(s): John Andersson, Georg S. Weiss
  • Journal Title: Journal fuer die Reine und Angewandte Mathematik 627 Pages: 213-235
  • Peer Reviewed
• [Journal Article] The two-phase membrane problem - Regularity in higher dimensions (2007)
  • Author(s): Henrik Shahgholian, Nina Uraltseva, Georg S. Weiss
  • Journal Title: Int. Math. Res. Not. Pages: doi:10.1093/imrn/rnm026, 1-16
  • Peer Reviewed
• [Journal Article] Self-propagating High temperature Synthesis in the high activation energy regime (2007)
  • Author(s): Regis Monneau, Georg S. Weiss
  • Journal Title: Acta Math. Univ. Comenianae 76(1) Pages: 99-109
  • Peer Reviewed
• [Journal Article] An unstable elliptic free boundary problem (2007)
  • Author(s): Regis Monneau, Georg S. Weiss
  • Journal Title: Duke Math. J. 136(2) Pages: 321-341
  • Peer Reviewed
• [Journal Article] Cross-shaped and degenerate singularities in an unstable elliptic free boundary problem (2006)
  • Author(s): John Andersson, Georg S. Weiss
  • Journal Title: J. Differential Equations 228(2) Pages: 633-640
  • Peer Reviewed
• [Journal Article] The two-phase membrane problem - an intersection-comparison approach to the regularity at branch points (2006)
  • Author(s): Henrik Shahgholian, Georg S. Weiss
  • Journal Title: Adv. Math. 205(2) Pages: 487-503
  • Peer Reviewed
• [Presentation] Geometric methods and generalized Stokes conjectures for water waves (2008)
  • Author(s): Georg S. Weiss
  • Organizer: Nordic-Russian Symposium in Honor of Vladimir Maz'ya
  • Place of Presentation: ストックホルム
  • Year and Date: 20080826-28
• [Presentation] A new frequency formula and applications to a singular perturbation problem (2008)
  • Author(s): Georg S. Weiss
  • Organizer: Viscosity Solutions in Partial Differential Equations
  • Place of Presentation: 京都
  • Year and Date: 20080625-27
• [Presentation] A Nonlinear Frequency Formula and the Singular set of a Free Boundary Problem (2008)
  • Author(s): Georg S. Weiss
  • Organizer: Free Boundary Problems - Theory and Applications
  • Place of Presentation: ストックホルム
  • Year and Date: 20080609-13
• [Presentation] A New Frequency Formula and the Singular Set of a Free Boundary Problem (2007)
  • Author(s): Georg S. Weiss
  • Organizer: Partielle Differentialgleichungen
  • Place of Presentation: Oberwolfach、ドイツ
  • Year and Date: 20070723-30
• [Presentation] A Parabolic Free Boundary Problem with Bernoulli type Condition on the Free Boundary (2007)
  • Author(s): Georg S. Weiss
  • Organizer: Geometry of Singularities
  • Place of Presentation: 仙台
  • Year and Date: 20070109-12
• [Presentation] Self-propagating High temperature Synthesis (SHS) in the High Activation Energy Regime (2006)
  • Author(s): Georg S. Weiss
  • Organizer: SIAM Conference on Analysis of Partial Differential Equations
  • Place of Presentation: ボストン
  • Year and Date: 20060710-12
• [Presentation] A Parabolic free boundary problem with Bernoulli type condition on the free boundary (2006)
  • Author(s): Georg S. Weiss
  • Organizer: Variational Problems and Related Topics
  • Place of Presentation: 京都
  • Year and Date: 20060620-22
• [Remarks] Math. Reviews Reviewer ホームページ
  • URL: http://www.ms.u-tokyo.ac.jp/.gw/