Related papers: Initial-boundary value problem for second order hy…
In this paper we study boundary value problems for higher order elliptic differential operators in divergence form. We consider the two closely related topics of inhomogeneous problems and problems with boundary data in fractional…
We propose methods that augment existing numerical schemes for the simulation of hyperbolic balance laws with Dirichlet boundary conditions to allow for the simulation of a broad class of differential algebraic conditions. Our approach is…
In this paper, we consider a doubly nonlinear parabolic equation $ \partial _t \beta (u) - \nabla \cdot \alpha (x , \nabla u) \ni f$ with the homogeneous Dirichlet boundary condition in a bounded domain, where $\beta : \mathbb{R} \to 2 ^{…
We consider a magnetic Schroedinger operator in a planar infinite strip with frequently and non-periodically alternating Dirichlet and Robin boundary conditions. Assuming that the homogenized boundary condition is the Dirichlet or the Robin…
We study the spectral behavior of higher order elliptic operators upon domain perturbation. We prove general spectral stability results for Dirichlet, Neumann and intermediate boundary conditions. Moreover, we consider the case of the…
The eigenvalue problem for the Laplacian on bounded, planar, convex domains with mixed boundary conditions is considered, where a Dirichlet boundary condition is imposed on a part of the boundary and a Neumann boundary condition on its…
We derive sharp estimates on the modulus of continuity for solutions of a large class of quasilinear isotropic parabolic equations on smooth metric measure spaces (with Dirichlet or Neumann boundary condition in case the boundary is…
We study a nonlinear elliptic boundary value problem defined on a smooth bounded domain involving the fractional Laplace operator, a concave-convex powers term together with mixed Dirichlet-Neumann boundary conditions.
We consider a singular perturbed eigenvalue problem for Laplace operator in a cylinder with frequent interchange of type of boundary condition on a lateral surface. These boundary conditions are prescribed by partition of lateral surface in…
We consider a (generally, non-coercive) mixed boundary value problem in a bounded domain $D$ of ${\mathbb R}^n$ for a second order parameter-dependent elliptic differential operator $A (x,\partial, \lambda)$ with complex-valued essentially…
We study second-order divergence-form systems on half-infinite cylindrical domains with a bounded and possibly rough base, subject to homogeneous mixed boundary conditions on the lateral boundary and square integrable Dirichlet, Neumann, or…
This note is a description of some of the results obtained by the authors in connection with the problem in the title. These, discussed following a summary of background material concerning wedge differential operators, consist of the…
The purpose of this article is to study quasi linear parabolic partial differential equations of second order, posed on a bounded network, satisfying a nonlinear and non dynamical Neumann boundary condition at the vertices. We prove the…
We consider the inverse problem for the second order self-adjoint hyperbolic equation in a bounded domain in $\R^n$ with lower order terms depending analytically on the time variable. We prove that, assuming the BLR condition, the…
Hyperbolic systems of the first and higher-order partial differential equations appear in many multiphysics problems. We will be dealing with a wave propagation problem in a piece-wise homogeneous medium. Mathematically, the problem is…
This paper investigates the existence of positive solutions for regular discrete second-order single-variable boundary value problems with mixed boundary conditions, including a nonhomogeneous Dirichlet boundary condition, of the form:…
End-point maximal $L^1$-regularity for parabolic initial-boundary value problems is considered. For the inhomogeneous Dirichlet and Neumann data, maximal $L^1$-regularity for initial-boundary value problems is established in time end-point…
Solution of Helmholtz equation with impedance boundary condition on finite interval is equivalently reformulated as steady state of initial boundary value problem for first order hyperbolic system of partial differential equations.…
In this paper, we establish the second order estimates of solutions to the first initial-boundary value problem for general Hessian type fully nonlinear parabolic equations on Riemannian manifolds. The techniques used in this article can…
We investigate a general nonhomogeneous parabolic initial-boundary value problem in some anisotropic H\"ormander inner product spaces. We prove that the operators corresponding to this problem are isomorphisms between appropriate…