Zobrazeno 1 - 10
of 97
pro vyhledávání: '"Gary M Lieberman"'
Autor:
Gary M Lieberman
This book gives an up-to-date exposition on the theory of oblique derivative problems for elliptic equations. The modern analysis of shock reflection was made possible by the theory of oblique derivative problems developed by the author. Such problem
Autor:
Sukjung Hwang, Gary M. Lieberman
Publikováno v:
Electronic Journal of Differential Equations, Vol 2015, Iss 288,, Pp 1-24 (2015)
Here we generalize quasilinear parabolic p-Laplacian type equations to obtain the prototype equation $$ u_t - \hbox{div} \Big(\frac{g(|Du|)}{|Du|} Du\Big) = 0, $$ where g is a nonnegative, increasing, and continuous function trapped in between
Externí odkaz:
https://doaj.org/article/18541866e37f4eee8b344cd9ccbcbaa1
Autor:
Sukjung Hwang, Gary M. Lieberman
Publikováno v:
Electronic Journal of Differential Equations, Vol 2015, Iss 287,, Pp 1-32 (2015)
Here we generalize quasilinear parabolic p-Laplacian type equations to obtain the prototype equation $$ u_t - \hbox{div} \Big(\frac{g(|Du|)}{|Du|} Du\Big) = 0, $$ where g is a nonnegative, increasing, and continuous function trapped in between
Externí odkaz:
https://doaj.org/article/f255cfc3bc534b2096b87d67f727c197
Autor:
Gary M. Lieberman
Publikováno v:
Communications in Partial Differential Equations. 45:1306-1318
We prove gradient bounds for solutions of a class of boundary value problems related to the capillary problem, using the maximum principle. Our results extend those of the author and those of Ma an...
Autor:
Gary M. Lieberman
Publikováno v:
Electronic Journal of Differential Equations, Vol 2000, Iss 38, Pp 1-17 (2000)
It is well-known that the maximum of the solution of a linear elliptic equation can be estimated in terms of the boundary data provided the coefficient of the gradient term is either integrable to an appropriate power or blows up like a small negativ
Externí odkaz:
https://doaj.org/article/bdbad21be19847398df95a18520933e1
Autor:
Gary M. Lieberman
Publikováno v:
Boundary Value Problems, Vol 2007 (2007)
We prove interior gradient estimates for a large class of parabolic equations in divergence form. Using some simple ideas, we prove these estimates for several types of equations that are not amenable to previous methods. In particular, we have no re
Externí odkaz:
https://doaj.org/article/da2d3e5d98044f7cb712ccf407b0aa23
Autor:
Gary M. Lieberman
Publikováno v:
Discrete and Continuous Dynamical Systems - Series B. 21:1525-1566
We show that solutions of equations of the form \[ -u_t+D_{11}u+(x^1)D_{22}u = f \] (and also more general equations in any number of dimensions) satisfy simple Holder estimates involving their derivatives. We also examine some pointwise properties f
Autor:
Gary M. Lieberman
Publikováno v:
Nonlinear Analysis: Theory, Methods & Applications. 119:382-397
We study a class of singular fully nonlinear elliptic equations under suitable natural conditions, with the model equation being Δ u + b ( γ ⋅ D u ) / d − u + c | D u | 2 = f for Lipschitz functions b > 0 , c and f , where d denotes distance to
Autor:
Gary M. Lieberman
Publikováno v:
Journal d'Analyse Mathématique. 115:213-249
In this paper, we study the asymptotic behavior of solutions of the problem Δpu = f (u) in Ω, u = ∞ on ∂Ω, under general conditions on the function f, where Ωp is the p-Laplace operator. We show that the technique used by the author for the s
Autor:
Gary M. Lieberman, Xing-Bin Pan
Publikováno v:
Proceedings of the Royal Society of Edinburgh: Section A Mathematics. 141:397-407
We examine the regularity of the solution of a quasilinear system involving the curl of vector fields. This system arises in the mathematical theory of superconductivity. The C2+α regularity was obtained by Bates and Pan under the condition that Ω