Results 1 to 10 of about 11,664 (312)
Gradient estimate for solutions of second-order elliptic equations [PDF]
Advances in Differential Equations, 2022 We obtain a local estimate for the gradient of solutions to a second-order elliptic equation in divergence form with bounded measurable coefficients that are square-Dini continuous at the single point x=0. In particular, we treat the case of solutions that are not Lipschitz continuous at x=0. We show that our estimate is sharp.
Maz'ya V., McOwen R.
openaire +4 more sources
Second order elliptic partial differential equations driven by Lévy white noise
Modern Stochastics: Theory and Applications, 2021 This paper deals with linear stochastic partial differential equations with variable coefficients driven by Lévy white noise. First, an existence theorem for integral transforms of Lévy white noise is derived and the existence of generalized and mild ...
David Berger, Farid Mohamed
doaj +1 more source
Second-Order Elliptic Equation with Singularities [PDF]
International Journal of Differential Equations, 2020 On the compact Riemannian manifold of dimension n≥5, we study the existence and regularity of nontrivial solutions for nonlinear second-order elliptic equation with singularities. At the end, we give a geometric application of the above singular equation.
openaire +2 more sources
On Second Order Elliptic Equations with a Small Parameter [PDF]
Communications in Partial Differential Equations, 2013 The Neumann problem with a small parameter $$(\dfrac{1}εL_0+L_1)u^ε(x)=f(x) \text{for} x\in G, .\dfrac{\partial u^ε}{\partial γ^ε}(x)|_{\partial G}=0$$ is considered in this paper. The operators $L_0$ and $L_1$ are self-adjoint second order operators. We assume that $L_0$ has a non-negative characteristic form and $L_1$ is strictly elliptic.
Freidlin, Mark, Hu, Wenqing
openaire +2 more sources
Second Order Differentiability for Solutions of Elliptic Equations in the Plane [PDF]
Journal of Mathematical Sciences, 2013 10 ...
McOwen, R., Maz'ya, V. G.
openaire +2 more sources
Second-order estimates for boundary blowup solutions of special elliptic equations
Boundary Value Problems, 2006 We find a second-order approximation of the boundary blowup solution of the equation , with , in a bounded smooth domain . Furthermore, we consider the equation .
Anedda Claudia +2 more
doaj +4 more sources
The oscillatory behavior of second order nonlinear elliptic equations
Electronic Journal of Qualitative Theory of Differential Equations, 2005 Some oscillation criteria are established for the nonlinear damped elliptic differential equation of second order $$ \sum_{i,\,j=1}^{N}D_i[\,a_{ij}(x)D_jy\,]+\sum_{i=1}^{N}b_i(x)D_iy+p(x)f(y)=0, \tag{E} $$ which are different from most known ones in ...
Zhiting Xu
doaj +1 more source
Compactness methods for Hölder estimates of certain degenerate elliptic equations
Electronic Journal of Qualitative Theory of Differential Equations, 2012 In this paper we obtain the interior $C^{1,\alpha}$ regularity of the quasilinear elliptic equations of divergence form. Our basic tools are the elementary local $L^\infty$ estimates and weak Harnack inequality for second-order linear elliptic equations,
Fengping Yao, Mijia Lai, Huilian Jia
doaj +1 more source
Asymptotic mean-value formulas for solutions of general second-order elliptic equations
Advanced Nonlinear Studies, 2022 We obtain asymptotic mean-value formulas for solutions of second-order elliptic equations. Our approach is very flexible and allows us to consider several families of operators obtained as an infimum, a supremum, or a combination of both infimum and ...
Blanc Pablo +3 more
doaj +1 more source
The multiscale perturbation method for second order elliptic equations
Applied Mathematics and Computation, 2020 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Alsadig Ali +3 more
openaire +3 more sources