Parabolic anisotropic problems with lower order terms and integrable data

Nonlinear Anisotropic Elliptic and Parabolic Equations in R with Advection and Lower Order Terms and Locally Integrable Data

We prove existence and regularity results for distributional solutions in RN for nonlinear elliptic and parabolic equations with general anisotropic diffusivities as well as advection and lower-order terms that satisfy appropriate growth conditions. The data are assumed to be merely locally integrable.

Renormalized Solutions for Strongly Nonlinear Elliptic Problems with Lower Order Terms and Measure Data in Orlicz-Sobolev Spaces

The purpose of this paper is to prove the existence of a renormalized solution of perturbed elliptic problems$ -operatorname{div}Big(a(x,u,nabla u)+Phi(u) Big)+ g(x,u,nabla u) = mumbox{ in }Omega,  $ in the framework of Orlicz-Sobolev spaces without any restriction on the $M$ N-function of the Orlicz spaces, where $-operatorname{div}Big(a(x,u,nabla u)Big)$ is a Leray-Lions operator defined f...

Title AN L^p-APPROACH TO SINGULAR LINEAR PARABOLIC EQUATIONS WITH LOWER ORDER TERMS

Exact Controllability for Problems of Transmission of the Plate Equation with Lower-order Terms

We consider the exact controllability for the problem of transmission of the plate equation with lower-order terms. Using Lions’ Hilbert Uniqueness Method (HUM for short), we show that the system is exactly controllable in L(Ω) ×H−2(Ω) . We also obtain some uniqueness theorems for the problem of transmission of the plate equation and for the operator a(x)∆ + q .

Finite element exterior calculus with lower-order terms

The scalar and vector Laplacians are basic operators in physics and engineering. In applications, they frequently show up perturbed by lowerorder terms. The effect of such perturbations on mixed finite element methods in the scalar case is well understood, but that in the vector case is not. In this paper, we first show that, surprisingly, for certain elements there is degradation of the conver...