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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Two families of $n$-rectangle nonconforming finite elements for sixth-order elliptic equations
六阶椭圆方程 矩形 有限元族
2023/4/13
We propose two families of nonconforming finite elements on $n$-rectangle meshes of any dimension to solve the sixth-order elliptic equations. The unisolvent property and the approximation ability of ...
The Harnack inequality for second-order elliptic equations with divergence-free drifts
Harnack inequality second-order elliptic equations divergence-free drifts
2015/7/14
We consider an elliptic equation with a divergence-free drift b. We prove that an inequality of Harnack type holds under the assumption b ∈ Ln/2+δ ∩ L2 where δ > 0. As an application we provide a one ...
Resonance and Landesman-Lazer condition for some Fully Nonlinear Elliptic equations
Resonance and Landesman-Lazer condition Nonlinear Elliptic equations
2015/4/3
Resonance and Landesman-Lazer condition for some Fully Nonlinear Elliptic equations.
PRINCIPAL CURVATURE ESTIMATES FOR THE CONVEX LEVEL SETS OF SEMILINEAR ELLIPTIC EQUATIONS
PRINCIPAL CURVATURE ESTIMATES THE CONVEX LEVEL SETS SEMILINEAR ELLIPTIC EQUATIONS
2014/4/3
We give a positive lower bound for the principal curvature of the strict convex level sets of harmonic functions in terms of the principal curvature of the domain boundary and the norm of the boundary...
Quasilinear elliptic equations and weighted Sobolev-Poincare inequalities with distributional weights
Quasilinear equations weighted integral inequalities elliptic regularity
2012/4/16
We introduce a class of weak solutions to the quasilinear equation $-\Delta_p u = \sigma |u|^{p-2}u$ in an open set $\Omega\subset\mathbf{R}^n$. Here $p>1$, and $\Delta_p u$ is the $p$-Laplacian opera...
Selected problems on elliptic equations involving measures
elliptic equations involving measures Analysis of PDEs
2012/4/18
This monograph concerns linear and nonlinear Dirichlet problems involving L^1 data and more generally measure data, based on Stampacchia's definition of weak solution. We explain some of the main tool...
Weighted Isoperimetric Inequalities and Applications to Elliptic Equations
Relative isoperimetric inequality weighted perimeter degenerate elliptic equations
2011/9/21
Abstract: In this paper we study some weighted isoperimetric inequalities relative to cones of $\mathbb{R}^{N}$. We give some information on the structure of those measures admitting as isoperimetric ...
Almgren-type monotonicity methods for the classification of behavior at corners of solutions to semilinear elliptic equations
Almgren monotonicity formula semilinear elliptic equations conical boundary points
2011/9/19
Abstract: A monotonicity approach to the study of the asymptotic behavior near corners of solutions to semilinear elliptic equations in domains with a conical boundary point is discussed. The presence...
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...
Cesari-type Conditions for Semilinear Elliptic Equations with Leading Term Containing Controls
optimal control existence conditions elliptic equations homogenization
2011/1/18
An optimal control problem governed by semilinear elliptic partial differential equations is con-sidered. The equation is in divergence form with the leading term containing controls. By studying the ...
On local analytic expansions of densities in the context of (micro-)hypoelliptic and classes of semi-elliptic equations
On local analytic expansions of densities context of (micro-)hypoelliptic classes of semi-elliptic equations
2011/1/17
Explicit representations of densities for linear parabolic partial differential equations are useful in order to design computation schemes of high accuracy for a considerable class of diffusion model...
By combining the formalism of \cite{RHE} with a discrete approach close to the considerations of \cite{Davie}, we interpret and solve the rough partial differential equation $dy_t=A y_t \, dt+\sum_{i=...
On non-local reflection for elliptic equations of the second order in R^2 (the Dirichlet condition)
elliptic equations the second order in R^2 (the Dirichlet condition)
2010/12/1
Point-to-point re
ection holding for harmonic functions subject to the Dirichlet or Neumann conditions on an analytic curve in the plane almost always fails for solutions to more general elliptic equ...
Local Estimates for Some Elliptic Equations Arising from Conformal Geometry
Local Estimates Elliptic Equations Arising Conformal Geometry
2018/4/19
We present some local gradient and Hessian estimates from C0 estimates for some elliptic equations arising from conformal deformations on the manifolds with totally geodesic boundary, which generalize...
Linear Elliptic Equations and Gauss Measure
Linear elliptic equation Comparison theorem Rearrangements of functions Gauss measure
2008/7/1
Linear Elliptic Equations and Gauss Measure.