2024/07/08 by Frisch, Michal Maria, Winkert, Patrick
#500 Naturwissenschaften und Mathematik::510 Mathematik::510 Mathematik #Robin and Steklov eigenvalues #boundedness results #convection term #coupled elliptic systems #equivalent norm #gradient dependence #nonlinear boundary condition #pseudomonotone operators
paper · doi:10.14279/depositonce-20930
In this paper, we study coupled elliptic systems with gradient dependent right-hand sides and nonlinear boundary conditions, where the left-hand sides are driven by so-called double phase operators. By applying a surjectivity result for pseudomonotone operators along with an equivalent norm in the function space, we prove that the system has at least one nontrivial solution under very general assumptions on the data. Under slightly stronger conditions, we are also able to show that this solution is unique. As a result of independent interest, we further prove the boundedness of solutions to such elliptic systems by employing Moser’s iteration scheme.