Free Boundary Problems and Monotonicity Formulas

• 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
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥3,760,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥360,000); Fiscal Year 2008: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2007: ¥1,400,000 (Direct Cost: ¥1,400,000); Fiscal Year 2006: ¥800,000 (Direct Cost: ¥800,000)
• 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 / 自由境界 / 単調性等式 / 正則性 / 燃焼理論の数学 / ステファン問題 / 進行波 / 特異極限 / SHS / 燃焼理論 / 特性極限 / Mumford-Shah汎関数 / 2相幕問題

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] A parabolic obstacle-problem-like equation (2009)
  • Author(s): Henrik Shahgholian, Nina Uraltseva, Georg S. Weiss
  • Journal Title: Advances in Mathematics 221 Pages: 861-881
  • Peer Reviewed
• [Journal Article] Pulsating traveling waves in the singular limit of a reaction?diffusion system in solid combustion (2008)
  • Author(s): Regis Monneau, Georg S. Weiss
  • Journal Title: Annales de 1' Institut Henri Poincare http://dx.doi.org/10.1016/j.anihpc.2008.09.002
  • 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.
  • 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] An unstable elliptic free boundary problem. (2007)
  • Author(s): Regis Monneau and G.S. Weiss
  • Journal Title: Duke Math. J. 136 Pages: 321-341
  • Peer Reviewed
• [Journal Article] Self-propagating High temperature Synthesis in the high activation energy regime. (2007)
  • Author(s): Regis Monneau and G.S. Weiss
  • Journal Title: Acta Math. Univ. Comenianae 76 Pages: 99-109
  • 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 8
  • Peer Reviewed
• [Journal Article] An unstable free boundary problem (2007)
  • Author(s): R.Monncau, G.S.Weiss
  • Journal Title: Duke Math.Journal 136・2 Pages: 321-341
• [Journal Article] Self-propagating High tempreature (2007)
  • Author(s): R.Monncau, G.S.Weiss
  • Journal Title: Acta math.Uaiv.Comenianae 96・1 Pages: 99-109
• [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
• [Journal Article] The two-phase membsane problem (2006)
  • Author(s): H.Shahgholian, G.S.Weiss
  • Journal Title: Advances in Mathematics 205・2 Pages: 487-503
• [Journal Article] Cross-shaped and degenecate singularities (2006)
  • Author(s): J.Andersson, G.S Weiss
  • Journal Title: Journal of Differential Equations 228・2 Pages: 633-640
• [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 Applic ations
  • Place of Presentation: ストックホルム
  • Year and Date: 2008-06-11
• [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
• [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
• [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
• [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
• [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
• [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
• [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
• [Remarks] Math. Reviews Reviewer ホームページ
  • URL: http://www.ms.u-tokyo.ac.jp/.gw/