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Results tagged with ap.analysis-of-pdes
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user 102331
Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.
2
votes
0
answers
156
views
geodesic balls in the conformal change
Consider a compact smooth Riemannian manifold $(\mathcal{M}, g)$. We consider a conformal change of the metric. Let $\tilde{g}=\phi g$, where $\phi$ is smooth and positive. Moreover, it satisfies $C_ …
- 103
7
votes
1
answer
345
views
is signed distance function real analytic for real analytic domains
If $\Omega$ is a real analytic domain in $\mathbb R^n$, is the signed distance function, $f$, defined by
\begin{equation}
f(x)=\begin{cases}d(x,\partial \Omega )&{\mbox{ if }}x\in \Omega \\-d(x,\parti …
- 103
0
votes
0
answers
258
views
The analyticity of distance function
Given a real analytic compact manifold $M$ with boundary $\partial M$, suppose that $M$ is embedded in an open analytic manifold $N$ which has the same dimension as $M$. Is the distance function $d(x …
- 103
1
vote
0
answers
229
views
Cauchy–Kowalevski Theorem for PDEs
I hope to extend the PDEs across the boundary using Cauchy–Kowalevski Theorem.
Given a real analytic manifold $M$ with boundary $\partial M$, the solution $u$ to the PDE $$\triangle u+b(x)\nabla u+c …
- 103