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Questions about partial differential equations of elliptic type. Often used in combination with the top-level tag ap.analysis-of-pdes.

4 votes
1 answer
512 views

solvability of linear elliptic pde on a torus

Consider a linear non-divergent form elliptic PDE on a flat torus $\mathbf{T}^n$, $$a_{ij}\partial_{ij}u+b_i\partial_iu=f$$ where all the coefficients and $f$ are smooth. What is the condition that en …