Fully nonlinear elliptic equations and Free boundary problem: Difference between pages

Latest revision as of 21:35, 15 April 2015

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-A fully nonlinear elliptic equation is an expression of the form
+#REDIRECT [[free boundary problems]]
-\[ F(D^2u, \nabla u, u, x) = 0 \text{ in } \Omega.\]
-The function $F$ is supposed to satisfy the following two basic assumptions
-* If $A \geq B$, $F(A,p,u,x) \geq F(B,p,u,x)$ for any values of $p \in \R^n$, $u\in \R$ and $x \in \Omega$.
-* If $u \geq v$, $F(A,p,u,x) \leq F(A,p,v,x)$ for any values of $A \in \R^{n \times n}$, $p \in \R^n$ and $x \in \Omega$.
-{{stub}}