Editing to a planar graph of given degrees

We consider the following graph modification problem. Let the input consist of a graph G=(V,E), a weight function w:V∪E→N, a cost function c:V∪E→N₀ and a degree function δ:V→N₀, together with three integers k_v, k_e and C. The question is whether we can delete a set of vertices of total weight at most k_v and a set of edges of total weight at most k_e so that the total cost of the deleted elements is at most C and every non-deleted vertex v has degree δ(v) in the resulting graph G^′. We also consider the variant in which G^′ must be connected. Both problems are known to be NP-complete and W[1]-hard when parameterized by k_v+k_e. We prove that, when restricted to planar graphs, they stay NP-complete but have polynomial kernels when parameterized by k_v+k_e.