Results 31 to 40 of about 216,973 (262)

Matrix Inequality for the Laplace Equation

, 2017
Since Li and Yau obtained the gradient estimate for the heat equation, related estimates have been extensively studied. With additional curvature assumptions, matrix estimates that generalize such estimates have been discovered for various time-dependent
Park, Jiewon
core   +1 more source

Surface stress calculations for nanoparticles and cavities in aluminum, silicon, and iron: influence of pressure and validity of the Young-Laplace equation

Materials Theory, 2021
This study is dedicated to the determination of the surface energy and stress of nanoparticles and cavities in presence of pressure, and to the evaluation of the accuracy of the Young-Laplace equation for these systems. Procedures are proposed to extract
Laurent Pizzagalli, Marie-Laure David
doaj   +1 more source

Sine-Laplace equation, sink - Laplace equation and harmonic maps

Manuscripta Mathematica, 1982
The relationship between harmonic maps from R2 to S2, H2, ST,1, S1,1(−1) and the ± sinh — Laplace, ± sine — Laplace equation is found respectively. Existence theorems of some boundary value problems for the above harmonic maps are obtained. In the cases of H2, S1,1(+1), S1,1(−1) the results are global.
openaire   +2 more sources

Precise Solution of Laplace's Equation [PDF]

Mathematics of Computation, 1995
An approximate method is described for solving Laplace’s equation \[ { Δ u = 0 u
Shi, Zhixin, Hassard, Brian
openaire   +2 more sources

Existence of solutions for a higher order non-local equation appearing in crack dynamics

, 2010
In this paper, we prove the existence of non-negative solutions for a non-local higher order degenerate parabolic equation arising in the modeling of hydraulic fractures.
A Mellet, Adachi J I Detournay E, Agranovich M S, Bernis F, Bernis F, Bernis F, Bernis F, Bertozzi A L, Bertsch M, C Imbert, Crouch S L, Dal Passo R, Dal Passo R, Grün G, Grün G, Lions J-L, Peirce A P, Zheltov Y P   +17 more
core   +1 more source

Probe method and a Carleman function

, 2020
A Carleman function is a special fundamental solution with a large parameter for the Laplace operator and gives a formula to calculate the value of the solution of the Cauchy problem in a domain for the Laplace equation.
Aizenberg L, Astala K, Astala K, Bateman H, Bateman H, Calderón A P, Cheng J, Evgrafov M A, Ikehata M, Ikehata M, Ikehata M, Ikehata M, Ikehata M, Ikehata M, Ikehata M, Ikehata M, Ikehata M, Ikehata M, Ikehata M, Kirsch A, Kress R, Masaru Ikehata, Vekua I N, Vekua I N, Yarmukhamedov Sh, Yarmukhamedov Sh, Yarmukhamedov Sh, Yarmukhamedov Sh   +27 more
core   +1 more source

A stochastic log-Laplace equation [PDF]

, 2003
We study a nonlinear stochastic partial differential equation whose solution is the conditional log-Laplace functional of a superprocess in a random environment. We establish its existence and uniqueness by smoothing out the nonlinear term and making use
Xiong, Jie
core   +2 more sources

Separation of Laplace’s equation [PDF]

Quarterly of Applied Mathematics, 1949
The following results are established in this paper: (I) ∗ ∗ ^{**} For the Laplace equation Δ θ = 0 \Delta \theta = 0 in curvilinear co-ordinates ( u , v , w ...
Levinson, N., Bogert, B., Redheffer, R. M.   +2 more
openaire   +1 more source

Robust Bio‐Textiles Via Mycelium‐Cellulose Interface Engineering

Advanced Functional Materials, EarlyView.
This work introduces a new class of sustainable textiles by growing mycelium, the root‐like structure of fungi, into cellulose‐based fabrics. This semi‐interpenetrating mycelium‐cellulose fiber network combines the strength and breathability of natural fibers with the water‐resistant and adhesive properties of mycelium, resulting in a robust, scalable,
Wenhui Xu, Qilong Cheng, Waqas Alam, Yanpei Tian, Pengfei Deng, Zhenyuan Niu, David Warsinger, Tian Li   +7 more
wiley   +1 more source

The Approximate Analytic Solution of the Time-Fractional Black-Scholes Equation with a European Option Based on the Katugampola Fractional Derivative

Mathematics, 2021
In the finance market, it is well known that the price change of the underlying fractal transmission system can be modeled with the Black-Scholes equation.
Sivaporn Ampun, Panumart Sawangtong
doaj   +1 more source