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We prove quantitative Runge type approximation results for spaces of smoothzero solutions of several classes of linear partial differential operators withconstant coefficients. Among others, we establish such results for arbitraryoperators on convex sets, elliptic operators, parabolic operators, and the waveoperator in one spatial variable. Our methods are inspired by the study oflinear topological invariants for kernels of partial differential operators. Asa part of our work, we also show a qualitative Runge type approximation theoremfor subspace elliptic operators, which seems to be new and of independentinterest.

Quantitative Runge type approximation theorems for zero solutions of certain partial differential operators