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We prove linear convergence for a new family of modified Dirichlet--Neumann methods applied to quasilinear parabolic equations, as well as the convergence of the Robin--Robin method. Such nonoverlapping domain decomposition methods are…
A procedure is described for defining a generalized solution for stochastic differential equations using the Cameron-Martin version of the Wiener Chaos expansion. Existence and uniqueness of this Wiener Chaos solution is established for…
We deal with a linear hyperbolic differential operator of the second order on a bounded planar domain with a smooth boundary. We establish a well-posedness result in case where a mixed, Dirichlet-Neumann, condition is prescribed on the…
In this paper, we study fully nonlinear second-order elliptic and parabolic equations with Neumann boundary conditions on compact Riemannian manifolds with smooth boundary. We derive oscillation bounds for admissible solutions with Neumann…
The diffuse domain method for partial differential equations on complicated geometries recently received strong attention in particular from practitioners, but many fundamental issues in the analysis are still widely open. In this paper we…
Initial-boundary value problems for second order fully nonlinear PDEs with Caputo time fractional derivatives of order less than one are considered in the framework of viscosity solution theory. Associated boundary conditions are Dirichlet…
Second order nonlinear eigenvalue problems are considered for which the spectrum is an interval. The boundary conditions are of Robin and Dirichlet type. The shape and the number of solutions are discussed by means of a phase plane…
We derive gradient and second order {\em a priori} estimates for solutions of the Neumann problem for a general class of fully nonlinear elliptic equations on compact Riemannian manifolds with boundary. These estimates yield regularity and…
The classical concept of $Q$-functions associated to symmetric and selfadjoint operators due to M.G. Krein and H. Langer is extended in such a way that the Dirichlet-to-Neumann map in the theory of elliptic differential equations can be…
We propose a new numerical method for the solution of the problem of the reconstruction of the initial condition of a quasilinear parabolic equation from the measurements of both Dirichlet and Neumann data on the boundary of a bounded…
We will study solvability of nonlinear second-order elliptic system of partial differential equations with nonlinear boundary conditions. We study the generalized Steklov Robin eigensystem (with possibly matrices weights) in which the…
The present work devoted to the finding explicit solution of a boundary problem with the Dirichlet-Neumann condition for elliptic equation with singular coefficients in a quarter of ball. For this aim the method of Green's function have…
We show that the knowledge of the Dirichlet-to-Neumann map on an arbitrary open portion of the boundary of a domain in $\mathbb{R}^n$, $n\ge 2$, for a class of semilinear elliptic equations, determines the nonlinearity uniquely.
In this paper, we study the nonhomogeneous Dirichlet problem concerning general semilinear elliptic equations in divergence form. We establish that the boundary Lipschitz regularity of solutions under some more weaker conditions on the…
Under structural conditions which are almost optimal, we derive a quantitative version of boundary estimate then prove existence of solutions to Dirichlet problem for a class of fully nonlinear elliptic equations on Hermitian manifolds.
Feynman's path integral is herein generalized to the nonextensive canonical density matrix based on Tsallis entropy. This generalization is done in two ways by using unnormalized and normalized constraints. Firstly, we consider the path…
Generalized Euler-Arnold-von Neumann density matrix equations can be solved by a binary Darboux transformation given here in a new form: $\rho[1]=e^{P\ln(\mu/\nu)}\rho e^{-P\ln(\mu/\nu)}$ where $P=P^2$ is explicitly constructed in terms of…
We establish some existence and regularity results to the Dirichlet problem, for a class of quasilinear elliptic equations involving a partial differential operator, depending on the gradient of the solution. Our results are formulated in…
This paper investigates two classes of quasilinear and essentially nonlinear integral equations with a sum-difference kernel on the half-line. Such equations arise in various areas of physics, including the theory of radiative transfer in…
A sharp pointwise differential inequality for vectorial second-order partial differential operators, with Uhlenbeck structure, is offered. As a consequence, optimal second-order regularity properties of solutions to nonlinear elliptic…