All Questions
8 questions
6
votes
2
answers
448
views
About the index theorems
I am looking for some introductory book/paper/notes about the several index theorems and their applications. By several I mean the "classical" Atiyah-Singer theorem, the local index theorem (...
- 789
5
votes
0
answers
878
views
A fourth-order linear PDE
I am interested in the following type of $4$-th order linear PDE with $2$ variables (i.e., $x$ and $t$):
$$x^3 f_{xxxt}+ f =0$$
Does anyone know if this type of PDE already appeared in the literature? ...
- 141
4
votes
3
answers
2k
views
book on PDE on manifolds
let $M$ be a Riemannian manifold and $\alpha$ be any some unknown form on $M$. I am interested in solutions or some references of the equation of type $(d + \delta) \alpha = 0$ where $\delta$ is the ...
- 89
4
votes
3
answers
473
views
Generalized Fuchsian-type PDE
Consider
$$
\big(1+ t\partial_t\big) \left(\partial^3_x+ {6\over x}\partial^2_x + {6\over x^2}\partial_x\right)A(x,t)+ {t\over (1-x)^3} A(x,t)=0
$$
with the initial condition $A(x,0)=1$. In a small $t$...
- 141
4
votes
0
answers
110
views
Regularity of the solution to a differential system with variable coefficients
Let $\Omega\subset \mathbb R^n$ be a convex subset. All the objects below will be defined on this set.
Let us assume $P(x,D)$ to be a differentiable operator order $m$ and of square size, that is ...
user17697
2
votes
1
answer
328
views
The study of dynamics of a polynomial vector field via Green's function methods
In the litterature, in particular in the papers on dynamical investigation of polynomial vector fields on the plane, are there some research devoting to study the Green's function for the PDE which is ...
- 356
2
votes
1
answer
215
views
Reference request for spectral theory of elliptic operators [closed]
I want to learn the spectral theory of linear elliptic operators in bounded and unbounded domains in $R^n$, in particular for Laplacian and Schrodinger operators. Please suggest me some reference.
I ...
1
vote
1
answer
442
views
Cauchy problem for an overdetermined system of PDE
This question is strictly related to this one. Let us consider the differential system with constant coefficients
$$\left(\begin{array}{ccc}
B_{11} & B_{12} & 0\\
...
- 277