The Experts below are selected from a list of 3945 Experts worldwide ranked by ideXlab platform
Ray Yang - One of the best experts on this subject based on the ideXlab platform.
-
Optimal Regularity and Nondegeneracy of a Free Boundary Problem Related to the Fractional Laplacian
Archive for Rational Mechanics and Analysis, 2013Co-Authors: Ray YangAbstract:We discuss the optimal regularity and Nondegeneracy of a free boundary problem related to the fractional Laplacian. This work is related to, but addresses a different problem from, recent work of C affarelli et al. (J Eur Math Soc (JEMS) 12(5):1151–1179, 2010 ). A variant of the boundary Harnack inequality is also proved, where it is no longer required that the function be zero along the boundary.
-
optimal regularity and Nondegeneracy of a free boundary problem related to the fractional laplacian
arXiv: Analysis of PDEs, 2011Co-Authors: Ray YangAbstract:We discuss the optimal regularity and Nondegeneracy of a free boundary problem related to the fractional Laplacian. This work is related to, but addresses a different problem from, recent work of Caffarelli, Roquejoffre, and Sire. A variant of the boundary Harnack inequality is also proved, where it is no longer required that the function be 0 along the boundary.
Changlin Xiang - One of the best experts on this subject based on the ideXlab platform.
-
Nondegeneracy of positive solutions to a kirchhoff problem with critical sobolev growth
Applied Mathematics Letters, 2018Co-Authors: Changlin XiangAbstract:Abstract In this paper, we prove uniqueness and Nondegeneracy of positive solutions to the following Kirchhoff equations with critical growth − a + b ∫ R 3 | ∇ u | 2 Δ u = u 5 , u > 0 in R 3 , where a , b > 0 are positive constants. This result has potential applications in singular perturbation problems concerning Kirchhoff equations.
-
Nondegeneracy of positive solutions to a kirchhoff problem with critical sobolev growth
arXiv: Analysis of PDEs, 2018Co-Authors: Changlin XiangAbstract:In this paper, we prove uniqueness and Nondegeneracy of positive solutions to the following Kirchhoff equations with critical growth \begin{eqnarray*} -\left(a+b\int_{\mathbb{R}^{3}}|\nabla u|^{2}\right)\Delta u=u^{5}, & u>0 & \text{in }\mathbb{R}^{3},\end{eqnarray*} where $a,b>0$ are positive constants. This result has potential applications in singular perturbation problems concerning Kirchhoff equaitons.
-
uniqueness and Nondegeneracy of ground states for choquard equations in three dimensions
Calculus of Variations and Partial Differential Equations, 2016Co-Authors: Changlin XiangAbstract:We obtain uniqueness and Nondegeneracy results for ground states of Choquard equations \(-\Delta u+u=\left( |x|^{-1}*|u|^{p}\right) |u|^{p-2}u\) in \(\mathbb {R}^{3}\), provided that \(p>2\) and p is sufficiently close to 2.
-
remarks on Nondegeneracy of ground states for quasilinear schrodinger equations
Discrete and Continuous Dynamical Systems, 2016Co-Authors: Changlin XiangAbstract:In this paper, we answer affirmatively the problem proposed by A. Selvitella in his work "Nondegeneracy of the ground state for quasilinear Schrodinger equations" (see Calc. Var. Partial Differential Equations, 53 (2015), 349-364): every ground state of the quasilinear Schrodinger equation \begin{eqnarray*}-\Delta u-u\Delta |u|^2+\omega u-|u|^{p-1}u=0&&\text{in }\mathbb{R}^N\end{eqnarray*} is nondegenerate for $1 0$ is a given constant and $N \ge1$.
Denis Bonheure - One of the best experts on this subject based on the ideXlab platform.
-
the logarithmic choquard equation sharp asymptotics and Nondegeneracy of the groundstate
Journal of Functional Analysis, 2017Co-Authors: Denis Bonheure, Silvia Cingolani, Jean Van SchaftingenAbstract:We derive the asymptotic decay of the unique positive, radially symmetric solution to the logarithmic Choquard equation −Δu+au=12π[ln1|x|⁎|u|2]uin R2 and we establish its Nondegeneracy. For the corresponding three-dimensional problem, the Nondegeneracy property of the positive ground state to the Choquard equation was proved by E. Lenzmann (2009) [13].
Guoyuan Chen - One of the best experts on this subject based on the ideXlab platform.
-
Nondegeneracy of ground states and multiple semiclassical solutions of the hartree equation for general dimensions
Results in Mathematics, 2021Co-Authors: Guoyuan ChenAbstract:We study Nondegeneracy of ground states of the Hartree equation $$ -\Delta u+u=(I_{2}*u^2)u\quad \text{ in } {\mathbb {R}}^n $$ where $$n=3,4,5$$ and $$I_2$$ is the Newton potential. As an application of the Nondegeneracy result, we use a Lyapunov–Schmidt reduction argument to construct multiple semiclassical solutions to the following Hartree equation with an external potential $$ -\varepsilon ^2\Delta u+u+V(x)u=\varepsilon ^{-2}(I_{2}*u^2)u\quad \text{ in } {\mathbb {R}}^n. $$
-
Nondegeneracy of ground states and multiple semiclassical solutions of the hartree equation for general dimensions
arXiv: Analysis of PDEs, 2016Co-Authors: Guoyuan ChenAbstract:We study Nondegeneracy of ground states of the Hartree equation $$ -\Delta u+u=(I_{2}\ast u^2)u\quad\mbox{ in }\mathbb R^n $$ where $n=3,4,5$ and $I_2$ is the Newton potential. As an application of the Nondegeneracy result, we use a Lyapunov-Schmidt reduction argument to construct multiple semiclassical solutions to the following Hartree equation with an external potential $$-\varepsilon^2\Delta u+u+V(x)u=\varepsilon^{-2}(I_{2}\ast u^2)u\quad \mbox{ in }\mathbb R^n.$$
Juncheng Wei - One of the best experts on this subject based on the ideXlab platform.
-
Nondegeneracy of nodal solutions to the critical yamabe problem
Communications in Mathematical Physics, 2015Co-Authors: Monica Musso, Juncheng WeiAbstract:We prove the existence of a sequence of nondegenerate, in the sense of Duyckaerts–Kenig–Merle [9], nodal nonradial solutions to the critical Yamabe problem $$-\Delta Q= |Q|^{\frac{2}{n-2}} Q, \quad Q \in {\mathcal D}^{1,2}(\mathbb{R}^n).$$ This is the first example in the literature of Nondegeneracy for nodal nonradial solutions of nonlinear elliptic equations and it is also the only nontrivial example for which the result of Duyckaerts–Kenig–Merle [9] applies.
-
Nondegeneracy of nonradial nodal solutions to yamabe problem
arXiv: Analysis of PDEs, 2014Co-Authors: Monica Musso, Juncheng WeiAbstract:We provide the first example of a sequence of {\em nondegenerate}, in the sense of Duyckaerts-Kenig-Merle \cite{DKM}, nodal nonradial solutions to the critical Yamabe problem $$ -\Delta Q= |Q|^{\frac{2}{n-2}} Q, \ \ Q \in {\mathcal D}^{1,2} (\R^n). $$