Non-local Gradient Dependent Operators
نویسنده
چکیده
In this paper we study a general class of “quasilinear non-local equations” depending on the gradient which arise from tug-of-war games. We establish a C/C/C regularity theory for these equations (the kind of regularity depending on the assumptions on the kernel), and we construct different non-local approximations of the p-Laplacian.
منابع مشابه
On nonlocal quasilinear equations and their local limits
We introduce a new class of quasilinear nonlocal operators and study equations involving these operators. The operators are degenerate elliptic and may have arbitrary growth in the gradient. Included are new nonlocal versions of p-Laplace, ∞-Laplace, mean curvature of graph, and even strongly degenerate operators. Our main results are non-trivial comparison, uniqueness, and existence results fo...
متن کاملNon-Local Morphological PDEs and p-Laplacian Equation on Graphs With Applications in Image Processing and Machine Learning
In this paper, we introduce a new class of nonlocal p-Laplacian operators that interpolate between non-local Laplacian and infinity Laplacian. These operators are discrete analogous of the game p-laplacian operators on Euclidean spaces, and involve discrete morphological gradient on graphs. We study the Dirichlet problem associated with the new p-Laplacian equation and prove existence and uniqu...
متن کاملA review of size-dependent elasticity for nanostructures
Nanotechnology is one of the pillars of human life in the future. This technology is growing fast and many scientists work in this field. The behavior of materials in nano size varies with that in macro dimension. Therefore scientists have presented various theories for examining the behavior of materials in nano-scale. Accordingly, mechanical behavior of nano-plates, nanotubes nano-beams and n...
متن کاملDynamic Stability of Single Walled Carbon Nanotube Based on Nonlocal Strain Gradient Theory
This paper deals with dynamic Stability of single walled carbon nanotube. Strain gradient theory and Euler-Bernouli beam theory are implemented to investigate the dynamic stability of SWCNT embedded in an elastic medium. The equations of motion were derived by Hamilton principle and non-local elasticity approach. The nonlocal parameter accounts for the small-size effects when dealing with nano-...
متن کاملEdge Detection and Extraction for SAR Images
Edge information is useful for various remote sensing applications : classification, relief reconstruction, image analysis. A lot of methods have been proposed to process edge extraction, with respect to the hypothesis of additive noise. All these methods are usually based on differential operators followed by a non local-maxima suppression or a zero-crossing search. In SAR imagery, presence of...
متن کامل