Motivated by a nonlocal free boundary problem, we study uniform properties of solutions to a singular perturbation problem for a boundary-reaction–diffusion equation, where the reaction term is of combustion type. This boundary problem is related to the fractional Laplacian. After an optimal uniform H¨older regularity is shown, we pass to the limit to study the free boundary problem it leads to.
|Number of pages||23|
|Journal||Nonlinear Analysis, Theory, Methods and Applications|
|Publication status||Published - 1 Jun 2016|
- Fractional/boundary reaction-diffusion problem
- Singular perturbation problem
- Uniform estimates