Homotopy principle (original) (raw)
편미분 방정식 이론에서, 호모토피 원리(homotopy原理, 영어: homotopy principle 호모토피 프린시플[*], h-principle 에이치 프린시플[*])는 특별한 편미분 방정식의 경우, 그 해의 존재 등의 성질이 호모토피 이론으로 결정된다는 성질이다.
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| dbo:abstract | In mathematics, the homotopy principle (or h-principle) is a very general way to solve partial differential equations (PDEs), and more generally (PDRs). The h-principle is good for underdetermined PDEs or PDRs, such as the immersion problem, isometric immersion problem, fluid dynamics, and other areas. The theory was started by Yakov Eliashberg, Mikhail Gromov and Anthony V. Phillips. It was based on earlier results that reduced partial differential relations to homotopy, particularly for immersions. The first evidence of h-principle appeared in the Whitney–Graustein theorem. This was followed by the Nash–Kuiper isometric C1 embedding theorem and the Smale–Hirsch immersion theorem. (en) 편미분 방정식 이론에서, 호모토피 원리(homotopy原理, 영어: homotopy principle 호모토피 프린시플[*], h-principle 에이치 프린시플[*])는 특별한 편미분 방정식의 경우, 그 해의 존재 등의 성질이 호모토피 이론으로 결정된다는 성질이다. (ko) H-принцип (читается аш-принцип) — общий способ решения дифференциальных уравнений в частных производных и, в более общем плане, дифференциальных соотношений в частных производных. Н-принцип хорош для недоопределённых систем, подобных тем, которые появляются в задачах о погружении, изометрическом погружении и других. Теория оформилась в работах Элиашберга, Громова и Филлипса. Основанием послужили более ранние результаты, в которых решение дифференциальных соотношений сводилось к гомотопии, в частности в задачах о погружениях. Первые идеи h-принципа появились в , парадоксе выворачивания сферы, теореме Нэша — Кёйпера и . (ru) |
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| rdfs:comment | 편미분 방정식 이론에서, 호모토피 원리(homotopy原理, 영어: homotopy principle 호모토피 프린시플[*], h-principle 에이치 프린시플[*])는 특별한 편미분 방정식의 경우, 그 해의 존재 등의 성질이 호모토피 이론으로 결정된다는 성질이다. (ko) In mathematics, the homotopy principle (or h-principle) is a very general way to solve partial differential equations (PDEs), and more generally (PDRs). The h-principle is good for underdetermined PDEs or PDRs, such as the immersion problem, isometric immersion problem, fluid dynamics, and other areas. (en) H-принцип (читается аш-принцип) — общий способ решения дифференциальных уравнений в частных производных и, в более общем плане, дифференциальных соотношений в частных производных. Н-принцип хорош для недоопределённых систем, подобных тем, которые появляются в задачах о погружении, изометрическом погружении и других. Теория оформилась в работах Элиашберга, Громова и Филлипса. Основанием послужили более ранние результаты, в которых решение дифференциальных соотношений сводилось к гомотопии, в частности в задачах о погружениях. (ru) |
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