partial differential equations with mixed boundary conditions - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-22T21:11:10Z http://mathoverflow.net/feeds/question/95062 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/95062/partial-differential-equations-with-mixed-boundary-conditions partial differential equations with mixed boundary conditions pascal 2012-04-24T19:39:15Z 2012-05-03T14:23:26Z <p>hi, </p> <p>does anyone know some good references (books, papers) on partial differential equations with mixed boundary conditions ?</p> <p>actually I am intrested in the following: Let $f(x)=(f_{1}(x),...,f_{n}(x))$ such that $x \in \mathbb{R}^{n}$ be an unknown function and denote by $J(f)$ the Jacobian of $f$. There is a first order partial non-linear equation, where $f$ is the unknown function, i.e. $F(J(f)(x),f(x),x)=g(x)$ (where one can assume that $F$ is "nice" and $g$ is some given "nice" function) on a domain $D$ in $\mathbb{R}^{n}$ such that $\partial D=C_{1} \cup C_{2}$. And the boundary conditions are: $f$ restricted to $C_{1}$ is zero and $J(f)$ restricted to $C_{2}$ is zero (as a matrix). Are there some references on such kind of equations ? </p> <p>Does anyone have an idea, about some references or this is to be solved ???</p> <p>pascal</p> http://mathoverflow.net/questions/95062/partial-differential-equations-with-mixed-boundary-conditions/95830#95830 Answer by lancy zhao for partial differential equations with mixed boundary conditions lancy zhao 2012-05-03T07:19:12Z 2012-05-03T07:19:12Z <p>Do you mean the partial differential equation like the Tricomi equation?</p>