Related papers: Integro-Differential Elliptic Equations
In this work we provide an Aleksandrov-Bakelman-Pucci type estimate for a certain class of fully nonlinear elliptic integro-differential equations, the proof of which relies on an appropriate generalization of the convex envelope to a…
In this book, there are five chapters: The Laplace Transform, Systems of Homogeneous Linear Differential Equations (HLDE), Methods of First and Higher Orders Differential Equations, Extended Methods of First and Higher Orders Differential…
Partial differential equations are ubiquitous in almost all applications of mathematics, where they provide a natural mathematical description of many phenomena involving change in physical, chemical, biological, and social processes. The…
We revisit the regularity theory for uniformly elliptic equations.
It is established existence, uniqueness and multiplicity of solutions for a quasilinear elliptic problem problems driven by $\Phi$-Laplacian operator. Here we consider the reflexive and nonreflexive cases using an auxiliary problem. In…
In this paper we study integro-differential equations like the anisotropic fractional Laplacian. As in [Silvestre, Indiana University Mathematics Journal 55, 2006], we adapt the De Giorgi technique to achieve the $C^{\gamma}$-regularity for…
Fractional-order elliptic problems are investigated in case of inhomogeneous Dirichlet boundary data. The boundary integral form is proposed as a suitable mathematical model. The corresponding theory is completed by sharpening the mapping…
Partial differential equations are fundamental tools in mathematics,sciences and engineering. This book is mainly an exposition of the various algebraic techniques of solving partial differential equations for exact solutions developed by…
We establish a new theory of regularity for elliptic complex valued second order equations of the form $\mathcal L=$div$A(\nabla\cdot)$, when the coefficients of the matrix $A$ satisfy a natural algebraic condition, a strengthened version…
This article presents a comprehensive overview and supplement to recent developments in second-order elliptic partial differential equations formulated in double divergence form, along with an exploration of their parabolic counterparts.
This work is devoted to the study of the existence and periodicity of solutions of initial differential problems, paying special attention to the explicit computation of the period. These problems are also connected with some particular…
We study weak solutions to nonlocal equations governed by integrodifferential operators. Solutions are defined with the help of symmetric nonlocal bilinear forms. Throughout this work, our main emphasis is on operators with general,…
In this paper we give a survey of elliptic theory for operators associated with diffeomorphisms of smooth manifolds. Such operators appear naturally in analysis, geometry and mathematical physics. We survey classical results as well as…
This paper deals with the existence of solutions for an elliptic system of partial differential equations. The solution method is based on the sub- and super-solutions approach. An application to a stochastic control problem is presented.…
The thesis studies linear and semilinear Dirichlet problems driven by different fractional Laplacians. The boundary data can be smooth functions or also Radon measures. The goal is to classify the solutions which have a singularity on the…
In one of his work, appeared in 1969, John A. Baker initiated the systematic investigation of some partial difference equations. The main purpose of this paper is to continue and to extend these investigations. Firstly, we present how such…
We extend the notion of viscosity solutions for path-dependent PDEs introduced by Ekren et al. [Ann. Probab. 42 (2014), no. 1, 204-236] to path-dependent integro-differential equations and establish well-posedness, i.e., existence,…
This paper focuses on the study of integro-differential equations with delays, presenting a novel perturbation approach. The primary objective is to introduce the concepts of classical and mild solutions for these equations and establish…
By the theory of pseudoinverse matrices and orthoprojectors, we establish a criterion for the solvability and find the general form of solutions of an integrodifferential equation with with impulse action and control. The general form of…
For scalar fully nonlinear partial differential equations depending on the Hessian andspatial coordinates, we present a general theory for obtaining comparison principles and well posedness for the associated Dirichlet problem with…