- Tytuł:
- Influence of an lp –perturbation on Hardy-Sobolev inequality with singularity a curve
- Autorzy:
-
Ijaodoro, Idowu Esther
Thiam, El Hadji Abdoulaye - Powiązania:
- https://bibliotekanauki.pl/articles/2050964.pdf
- Data publikacji:
- 2021
- Wydawca:
- Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
- Tematy:
-
Hardy-Sobolev inequality
positive minimizers
parametrized curve
mass
Green function - Opis:
- We consider a bounded domain $\Omega~\text{of}~\mathbb{R}^{N}, N \geq 3, h \text{and} b$ continuous functions on $\Omega$. Let $Gamma$ be a closed curve contained in $\Omega$. We study existence of positive solutions $u \in H_{0}^{1}(\Omega)$ to the perturbed Hardy-Sobolev equation: $$-\Delta{}u + hu + bu^{1+\delta} = \rho_{\Gamma}^{-\sigma} u^{2_{\sigma}^{\star}-1}~\text{in}~\Omega,$$ where $2_{\sigma}^{\star} := \frac{2(N-\sigma)}{N-2}$ is the critical Hardy-Sobolev exponent $\sigma \in [0,2), 0 < \delta < \frac{4}{N-2}$ and $\rho_{\Gamma}$ is the distance function to $\Gamma$. We show that the existence of minimizers does not depend on the local geometry of $\Gamma$ nor on the potential $h$. For $N = 3$, the existence of ground-state solution may depends on the trace of the regular part of the Green function of $-\Delta + h$ and or on $b$. This is due to the perturbative term of order $1 + \delta$.
- Źródło:
-
Opuscula Mathematica; 2021, 41, 2; 187-204
1232-9274
2300-6919 - Pojawia się w:
- Opuscula Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł