{\displaystyle \Delta _{\infty }u(x)={\frac {\langle Du,D^{2}u\,Du\rangle }{|Du|^{2}}}={\frac {1}{|Du|^{2}}}\sum _{i,j}{\frac {\partial ^{2}u}{\partial x_{i}\,\partial x_{j}}}{\frac {\partial u}{\partial x_{i}}}{\frac {\partial u}{\partial x_{j}}}.}
The first version avoids the singularity which occurs when the gradient vanishes, while the second version is homogeneous of order zero in the gradient. Verbally, the second version is the second derivative in the direction of the gradient. In the case of the infinity Laplace equation
Δ
∞
u
=
0
{\displaystyle \Delta _{\infty }u=0}
, the two definitions are equivalent.
While the equation involves second derivatives, usually (generalized) solutions are not twice differentiable, as evidenced by the well-known Aronsson solution
u
(
x
,
y
)
=
|
x
|
4
/
3
−
|
y
|
4
/
3
{\displaystyle u(x,y)=|x|^{4/3}-|y|^{4/3}}
. For this reason the correct notion of solutions is that given by the viscosity solutions.
Viscosity solutions to the equation
Δ
∞
u
=
0
{\displaystyle \Delta _{\infty }u=0}
are also known as infinity harmonic functions. This terminology arises from the fact that the infinity Laplace operator first arose in the study of absolute minimizers for
‖
D
u
‖
L
∞
{\displaystyle \|Du\|_{L^{\infty }}}
, and it can be viewed in a certain sense as the limit of the p-Laplacian as
p
→
∞
{\displaystyle p\rightarrow \infty }
. More recently, viscosity solutions to the infinity Laplace equation have been identified with the payoff functions from randomized tug-of-war games. The game theory point of view has significantly improved the understanding of the partial differential equation itself.
Hi guys. May tanong sana ako about this infinity sim plan. Nabili ko to 2 weeks ago. Inclusions daw eh unli data, unli trinet call and text. May consumable 2400 din.
Kahapon (May 31) ko lang na notice na parang regular load yung consumption ko sa data, calls, at text. Pataas at pataas yung...
Hi, may nakita ako sa shoppee P3K Smart sim with unlimited data daw. Nasa 2500 ata ang monthly. Legit ba to? If meron kayong alam na legit na nag offer nito, I think corporate sim tawag nito, please tell me? Salamat.
may nabili kasi ako na smart corpo sim not sure kng smart corpo sim talaga or infinity siya kasi nakalagay Revamp consumable plan 800mg
pero unli data nman hanggang ngayon ok pa nman.
Gusto ko lang malaman if panu malaman if smart corpo ba siya or infinity sim?
at ask lang din ako ano ang...
Good pm po mga boss. Tatanong ko lang po, kung ano ung pwede kong maging assurance sa pagbili ng black mamba modem kung tawagin? Smart infinity sim po gamit ko. Makakalaro na kaya ako ng online games nun? Thank u po sa magrreply. :)
so yung globe infinity ko ay walang number bawal mag text o call. ang tanong ko lang is kung pwede ko ba gamitan ng vpn para mas bumilis speed ko? kasi dito sa sampaloc ngayon sobrang bagal na ng globe. smart ang mabilis dito. salamat sa sasagot
Magandang araw mga boss.
Tanong ko laang po kung ano ang pinagkaiba ng Smart Infinity Sim sa Smart Corpo Sim, alin ang mas maganda sa dalawa at may capping ba ang mga ito?? Bakit sa Smart Corpo Sim, sa mismong tao ka magbabayad while sa Smart Infinity Sim, ok lang na sa mga bayad center...
As ko lang guys about sa infinity sim.Meron kasi nagbibentA bali 3,500 cashout mo tapos may 1,700 ka pang babayaran.Pano po ba ang takbo ng Infinity sim Just Curious lang po Nandiyan po sa image.
Need help lang po curious lang Explain niyo po sa akin.
Hi po, may nabasa po ako na simula nov.28 mag iiba na po data charging nang smart. Ang focus ko po ay Kung ilan na po real speed nyo if throttled na kayo. Base po sa post nang nabasa ko ay pag na reach na po ninyo ang allowance nyo sa ABS na 2500 ay mag throttle speed nyo sa 128Kbps na ang ibig...
Guys willing akong bumili ng infinity sim basta ma met nya tong mga requirements:
50-80MBPS
UNLIMITED INTERNET
No Capping
No Monthly
12 Months Validity
No Need Load
No Need Refresh
Yun lang thank you mga boss. kung may mali sa post ko pakisabi nalang ayusin ko agad ty
may nakita ko po na seller ng globe postpaid sim. 3 months daw connected. legit ba ito? may naka bili na dito sa kanya?
FB username: Nathaniel Alastair Gavilan
naka attach po yung screenshots
thanks in advance po