Results 111 to 120 of about 3,789 (142)

Smoothness of solutions of almost hypoelliptic equations

Journal of Contemporary Mathematical Analysis, 2009
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On Solvability of Regular Hypoelliptic Equations in ℝn

Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences), 2018
In this paper the unique solvability of regular hypoelliptic equations in multianisotropic weighted functional spaces is proved by means of special integral representation of functions through a regular operator. The existence of the solutions is proved by constructing approximate solutions using multianisotropic integral operators.
G. A. Karapetyan, H. A. Petrosyan
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Stochastic Differential Equations and Hypoelliptic Operators

2004
The first half of the twentieth century saw some remarkable developments in analytic probability theory. Wiener constructed a rigorous mathematical model of Brownian motion. Kolmogorov discovered that the transition probabilities of a diffusion process define a fundamental solution to an associated heat equation.
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Hypoelliptic overdetermined systems of partial differential equation

Communications in Partial Differential Equations, 1980
(1980). Hypoelliptic overdetermined systems of partial differential equation. Communications in Partial Differential Equations: Vol. 5, No. 4, pp. 331-380.
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Anisotropic function spaces and related semi–linear hypoelliptic equations

Mathematische Nachrichten, 2003
AbstractLooking for the best possible smoothness (in terms of the upper index of the Besov spaces) for the solution of some semi–linear equations we consider a model case of a hypoelliptic operator, which acts between anisotropic Besov spaces. To obtain the best regularity we need some properties for the corresponding spaces, which we prove here.
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Global hypoelliptic estimates for fractional order kinetic equation

Mathematische Nachrichten, 2013
In this paper we study a class of fractional order kinetic equation, which is a linear model of spatially inhomogeneous Boltzmann equation without angular cutoff. Using the multiplier method introduced by F. Hérau and K. Pravda‐Starov (J. Math. Pures et Appl., 2011), we establish the optimal global hypoelliptic estimates with weights for the linear ...
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Hypoellipticity of Ito’s Second Order Parabolic Equations

1990
0.1. Smoothness of solutions of deterministic parabolic equations increases as the smoothness assumptions on their coefficients increase. This is a typical feature of parabolic equations. Moreover, under wide assumptions, the smoothness of solutions for t>0 depends only on the smoothness of coefficients and does not depend on the smoothness of the ...
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Solving integral equations in free space with inverse-designed ultrathin optical metagratings

Nature Nanotechnology, 2023
Andrea Cordaro, Andrea Alu
exaly  

DeepXDE: A Deep Learning Library for Solving Differential Equations

SIAM Review, 2021
Lu Lu, George E Karniadakis
exaly  

An energy approach to the solution of partial differential equations in computational mechanics via machine learning: Concepts, implementation and applications

Computer Methods in Applied Mechanics and Engineering, 2020
Esteban Samaniego, Somdatta Goswami, Timon Rabczuk   +2 more
exaly