About: Semi-elliptic operator

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In mathematics — specifically, in the theory of partial differential equations — a semi-elliptic operator is a partial differential operator satisfying a positivity condition slightly weaker than that of being an elliptic operator. Every elliptic operator is also semi-elliptic, and semi-elliptic operators share many of the nice properties of elliptic operators: for example, much of the same existence and uniqueness theory is applicable, and semi-elliptic Dirichlet problems can be solved using the methods of stochastic analysis.

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  • In mathematics — specifically, in the theory of partial differential equations — a semi-elliptic operator is a partial differential operator satisfying a positivity condition slightly weaker than that of being an elliptic operator. Every elliptic operator is also semi-elliptic, and semi-elliptic operators share many of the nice properties of elliptic operators: for example, much of the same existence and uniqueness theory is applicable, and semi-elliptic Dirichlet problems can be solved using the methods of stochastic analysis. (en)
  • 数学の、特に偏微分方程式の理論において、半楕円型作用素（はんだえんがたさようそ、英: semi-elliptic operator）とは、楕円型作用素のそれよりもわずかに弱い正値性の条件を満たすある偏微分作用素のことを言う。すべての楕円型作用素は半楕円型でもあり、楕円型作用素の持つ多くの良い性質を半楕円型作用素も持つ。例えば、存在や一意性の理論の多くは同一のものが適用可能で、半楕円型ディリクレ問題はを利用することで解くことが出来る。 (ja)
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  • In mathematics — specifically, in the theory of partial differential equations — a semi-elliptic operator is a partial differential operator satisfying a positivity condition slightly weaker than that of being an elliptic operator. Every elliptic operator is also semi-elliptic, and semi-elliptic operators share many of the nice properties of elliptic operators: for example, much of the same existence and uniqueness theory is applicable, and semi-elliptic Dirichlet problems can be solved using the methods of stochastic analysis. (en)
  • 数学の、特に偏微分方程式の理論において、半楕円型作用素（はんだえんがたさようそ、英: semi-elliptic operator）とは、楕円型作用素のそれよりもわずかに弱い正値性の条件を満たすある偏微分作用素のことを言う。すべての楕円型作用素は半楕円型でもあり、楕円型作用素の持つ多くの良い性質を半楕円型作用素も持つ。例えば、存在や一意性の理論の多くは同一のものが適用可能で、半楕円型ディリクレ問題はを利用することで解くことが出来る。 (ja)
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  • 半楕円型作用素 (ja)
  • Semi-elliptic operator (en)
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