Best possible estimates of weak solutions of boundary value problems for quasi-linear elliptic equations in unbounded domains

We investigate the behaviour of weak solutions of boundary value problems for quasi-linear elliptic divergence second order equations in unbounded domains. We show the boundedness of weak solutions to our problem. Using barrier function and applying the comparison principle, we find the exact exponent of weak solutions decreasing rate near the infinity.

The Behaviour of Weak Solutions of Boundary Value Problems for Linear Elliptic Second Order Equations in Unbounded Cone-Like Domains

We investigate the behaviour of weak solutions of boundary value problems (Dirichlet, Neumann, Robin and mixed) for linear elliptic divergence second order equations in domains extending to infinity along a cone. We find an exponent of the solution decreasing rate: we derive the estimate of the weak solution modulus for our problems near the infinity under assumption that leading coefficients of the equations do not satisfy the Dini-continuity condition.

Nonlocal Robin Problem for Elliptic Quasilinear Second Order Equations

We investigate the behavior of weak solutions to the nonlocal Robin problem for quasilinear elliptic divergence second order equations in a neighborhood of the boundary corner point. We find an exponent of the solution decreasing rate near the boundary corner point.

Boundary value problems for quasi-linear elliptic second order equations in unbounded cone-like domains

We study the behaviour of weak solutions (as well as their gradients) of boundary value problems for quasi-linear elliptic divergence equations in domains extending to infinity along a cone.