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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Laplacian estimates for the cscK equation
cscK方程 拉普拉斯估计 Nash-Moser迭代
2023/11/29
We will report Chen-Cheng’s work on cscK equations. We derive the Laplacian bound using Nash-Moser iteration.
利用H增生映射的性质，证明了含有广义（p，q）-Laplacian算子的非线性椭圆系统存在唯一解的结论.证明方法简单且研究结果展示了H增生映射和非线性椭圆系统之间的关系，推广和补充了以往的相关研究工作.
Singular parabolic p-Laplacian systems under non-smooth external forces. Regularity up to the boundary
Initial-boundary value problems p-Laplacian parabolic singular systems regularity up to the boundary
2012/6/30
We study the regularity of the solutions to initial-boundary value problems for N-systems of the p-Laplacian type, in $n\geq 3$ space variables, with square-integrable external forces in the space-tim...
Symmetry results for the $p(x)$-Laplacian equation
Quasi-linear elliptic equations p(x)-Laplacian operator symmetrization partial symmetry
2012/6/25
We consider the Dirichlet problem for the nonlinear $p(x)$-Laplacian equation. For axially symmetric domains we prove that, under suitable assumptions, there exist Mountain-pass solutions which exhibi...
Geometrical structure of Laplacian eigenfunctions
Laplace operator eigenfunctions eigenvalues localization
2012/6/25
We review the properties of eigenvalues and eigenfunctions of the Laplace operator in bounded Euclidean domains with Dirichlet, Neumann or Robin boundary condition. We keep the presentation at a level...
Multiplicity of 1D-concentrating positive solutions to the Dirichlet problem for equation with $p$-Laplacian
Multiplicity of 1D-concentrating positive solutions Dirichlet problem equation Analysis of PDEs
2012/6/21
We prove the multiplicity of spike-layer type solutions to the Dirichlet problem for the equation $-\Delta_p u = u^{q-1}$ in expanding annuli.
Long-time dynamics of the parabolic $p$-Laplacian equation
p-Laplacian equation attractors Long-time dynamics
2012/2/29
In this paper, we study the long-time behaviour of solutions of Cauchy problem for the parabolic $p$-Laplacian equation with variable coefficients. Under mild conditions on the coefficient of the prin...
Correctors and Field Fluctuations for the $p_ε(x)$-Laplacian with Rough Exponents: Cases$1 p_2\leq 2$ and $1 p_2$
correctors dispersed media homogenization layered media plaplacian periodic domain power-law materials young measures
2011/9/9
Abstract: A corrector theory for the strong approximation of fields inside composites made from two materials with different power law behavior is provided. The correctors are used to develop bounds o...
$H^2$ regularity for the $p(x)-$Laplacian in two-dimensional convex domains
Variable exponent spaces Elliptic Equations H2 regularity
2011/9/9
Abstract: In this paper we study the $H^2$ global regularity for solutions of the $p(x)-$Laplacian in two dimensional convex domains with Dirichlet boundary conditions. Here $p:\Omega \to [p_1,\infty)...
Saddle-shaped solutions of bistable elliptic equations involving the half-Laplacian
Half-Laplacian saddle-shaped solutions asymptotic behaviour stability properties
2011/9/2
Abstract: We establish existence and qualitative properties of saddle-shaped solutions of the elliptic fractional equation $(-\Delta)^{1/2}u=f(u)$ in all the space $\re^{2m}$, where $f$ is of bistable...
Existence and multiplicity of solutions to equations of $N-$Laplacian type with critical exponential growth in $\mathbb{R}^{N}$
Ekeland variational principle Mountain-pass Theorem Variational methods Critical growth Moser-Trudinger inequality
2011/8/23
Abstract: In this paper, we deal with the existence and multiplicity of solutions to the nonuniformly elliptic equation of the N-Lapalcian type with a potential and a nonlinear term of critical expone...
Laplacian Growth, Elliptic Growth, and Singularities of the Schwarz Potential
Laplacian Growth Elliptic Growth Singularities Schwarz Potential
2010/12/13
The Schwarz function has played an elegant role in understanding and in generating new examples of exact solutions to the Laplacian growth (or \Hele-Shaw\) problem in the plane.
Degenerate homogeneous parabolic equations associated with the infinity-Laplacian
Degenerate homogeneous parabolic equations infinity-Laplacian
2010/12/8
We prove existence and uniqueness of viscosity solutions to the degenerate parabolic problem ut = h 1u where h 1 is the h-homogeneous operator associated with the infinity-Laplacian, h 1u = |Du|h&#...