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Results tagged with ap.analysis-of-pdes
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user 132031
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
1
answer
257
views
Eigenvalue problem involving fractional laplacian
Does the problem
$$(-\Delta)^s u=\lambda u \text{ in } \mathbb R^N $$ admit a non-trivial solution when $s\in (0, 1)$ and $\lambda>0.$
- 63
4
votes
0
answers
187
views
Sobolev embedding in an annulus
Is it possible to determine the best constant $S(\Omega, p)$ of the embedding $H^1_{0, r}(\Omega)$ to $L^{p+1}(\Omega)$ where $p>1$ and $\Omega=\{a<|x|<b\}.$
- 63