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hi,

does anyone know some good references (books, papers) on partial differential equations with mixed boundary conditions ?

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 ?

Does anyone have an idea, about some references or this is to be solved ???

pascal

edited May 3 2012 at 14:23

Willie Wong
6,987●20●43

asked Apr 24 2012 at 19:39

pascal
47●3

Yes, I do...... – András Bátkai Apr 24 2012 at 21:52

What do you mean by mixed boundary conditions? – timur Apr 24 2012 at 22:07

2

Your question is far to vague. Can you specify what you are interested in? – András Bátkai Apr 25 2012 at 6:06

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 $D$ such that $\partial D = C_{1} \cup C_{2}$. And the boundary conditions are: $f|_{C_{1}} = 0$ and $J(f)|_{C_{2}} = 0$. Are there some references on such kind of equations ? – pascal Apr 25 2012 at 14:13

I think it should be clear now, what I mean ? Or ? – pascal Apr 26 2012 at 6:11

show 5 more comments

lancy zhao · Answer 1 · 2012-05-03 07:19:12Z UTC

-1

Do you mean the partial differential equation like the Tricomi equation?

answered May 3 2012 at 7:19

lancy zhao
1

	From the comments, the equation is fully nonlinear. So no, I don't think it is like the Tricomi equation. – Willie Wong May 3 2012 at 9:11
	Sorry because I know little about it,and I'm also looking for some reference about the topic.Do you have any to recommend? Why can't I give a boudary condition of mixed type to a fully nonlinear equation?What if I make a Legendre transformation? – lancy zhao May 4 2012 at 10:29

partial differential equations with mixed boundary conditions

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