Transmission Robin problem for singular p(x)-Laplacian equation in a cone

We study the behavior near the boundary angular or conical point of weak solutions to the transmission Robin problem for an elliptic quasi-linear second-order equation with the variable p(x)-Laplacian

The Dirichlet problem in an unbounded cone-like domain for second order elliptic quasilinear equations with variable nonlinearity exponent

In this paper we consider the Dirichlet problem for quasi-linear second-order elliptic equation with the m(x)-Laplacian and the strong nonlinearity on the right side in an unbounded cone-like domain. We study the behavior of weak solutions to the problem at infinity and we find the sharp exponent of the solution decreasing rate. We show that the exponent is related to the least eigenvalue of the eigenvalue problem for the Laplace–Beltrami operator on the unit sphere

The Robin problem for singular p(x)-Laplacian equation in a cone

We study the behavior near the boundary angular or conical point of weak solutions to the Robin problem for an elliptic quasi-linear second-order equation with the variable p(x)-Laplacian

Existence of bounded weak solutions of the Robin problem for a quasi-linear elliptic equation with p(x)-Laplacian

We prove the existence of bounded weak solutions to the Robin problem for an elliptic quasi-linear second-order equation with the variable $p(x)$-Laplacian

The Robin problem for singular p(x)p(x)-Laplacian equation in a cone

We study the behavior near the boundary angular or conical point of weak solutions to the Robin problem for an elliptic quasi-linear second-order equation with the variable $p(x)$-Laplacian

L-infinity-estimate for the Robin problem of a singular variable p-Laplacian equation in a conical domain

We establish a bound for the modulus of the weak bounded solution to the Robin problem for an elliptic quasi-linear second-order equation with the variable p(x)-Laplacian

Transmission Problems for Elliptic Second-Order Equations in Non-Smooth Domains

The goal of this book is to investigate the behaviour of weak solutions to the elliptic transmisssion problem in a neighborhood of boundary singularities: angular and conic points or edges. We consider this problem both for linear and quasi-linear (till now very little studied) equations. Chapter 1 is of auxiliary character. Chapter 2 deals with the eigenvalue problem for the m-Laplace-Beltrami operator. By the variational principle we prove a new integro-differential Friedrichs-Wirtinger type inequality. This inequality is a basis for the obtaining of precise exponents of the decreasing rat

Transmission Robin problem for singular p(x)p(x)-Laplacian equation in a cone

We study the behavior near the boundary angular or conical point of weak solutions to the transmission Robin problem for an elliptic quasi-linear second-order equation with the variable $p(x)$-Laplacian

Dini continuity of the first derivatives of generalized solutions to the Dirichlet problem for linear elliptic second order equations in nonsmooth domains

We consider generalized solutions to the Dirichlet problem for linear elliptic second order equations in a domain bounded by a Dini-Lyapunov surface and containing a conical point. For such solutions we derive Dini estimates for the first order generalized derivatives

The Dirichlet problem in an unbounded cone-like domain for second order elliptic quasilinear equations with variable nonlinearity exponent

In this paper we consider the Dirichlet problem for quasi-linear second-order elliptic equation with the $m(x)$-Laplacian and the strong nonlinearity on the right side in an unbounded cone-like domain. We study the behavior of weak solutions to the problem at infinity and we find the sharp exponent of the solution decreasing rate. We show that the exponent is related to the least eigenvalue of the eigenvalue problem for the Laplace–Beltrami operator on the unit sphere