共查询到20条相似文献,搜索用时 31 毫秒
1.
Thomas Strömberg 《Archiv der Mathematik》2010,94(6):579-589
We present sharp Hessian estimates of the form D2 Se(t,x) £ g(t)I{D^2 S^\varepsilon(t,x)\leq g(t)I} for the solution of the viscous Hamilton–Jacobi equation
llSet+\frac12|DSe|2+V(x)-eDSe = 0 in QT=(0,T]× \mathbb Rn, Se(0,x) = S0(x) in \mathbb Rn.\begin{array}{ll}S^\varepsilon_t+\frac{1}{2}|DS^\varepsilon|^2+V(x)-\varepsilon\Delta S^\varepsilon = 0\quad {\rm in} \, Q_T=(0,T]\times\, {\mathbb {R}^n}, \\ \qquad \qquad \qquad \qquad \quad \, S^\varepsilon(0,x) = S_0(x)\quad{\rm in}\, {\mathbb {R}^n}.\end{array} 相似文献
2.
We study the family of divergence-type second-order parabolic equations
we(x)\frac?u?t=div(a(x)we(x) ?u), x ? \mathbbRn{\omega_\varepsilon(x)\frac{\partial u}{\partial t}={\rm div}(a(x)\omega_\varepsilon(x) \nabla u), x \in \mathbb{R}^n} , with parameter ${\varepsilon >0 }${\varepsilon >0 } , where a(x) is uniformly elliptic matrix and we=1{\omega_\varepsilon=1} for x
n
< 0 and we=e{\omega_\varepsilon=\varepsilon} for x
n
> 0. We show that the fundamental solution obeys the Gaussian upper bound uniformly with respect to e{\varepsilon} . 相似文献
3.
In the Euclidean Space
\mathbb Rn+1{\mathbb {R}^{n+1}} with a density
ee\frac12 n m2 |x|2, (e = ±1){e^{\varepsilon \frac12 n \mu^2 |x|^2},} {(\varepsilon =\pm1}), we consider the flow of a hypersurface driven by its mean curvature associated to this density. We give a detailed account
of the evolution of a convex hypersurface under this flow. In particular, when e = -1{ \varepsilon=-1} (Gaussian density), the hypersurface can expand to infinity or contract to a convex hypersurface (not necessarily a sphere)
depending on the relation between the bound of its principal curvatures and μ. 相似文献
4.
Egor A. Alekhno 《Positivity》2012,16(1):143-176
Let A be an ordered Banach algebra. Put
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