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Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.

6 votes
1 answer
153 views

Laplacian is surjective from $\mathcal{C}^{\infty}(B)$ to $\mathcal{C}^{\infty}(B)$

Let $B$ denote the open unit ball in $\mathbb{R}^n$. Let $\mathcal{C}^{\infty}(B)$ represent the space of smooth functions on $B$. Is the Laplacian operator $\Delta$ surjective as a map from $\mathcal …
Jessie L's user avatar