Partial Differential Equations

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2 domain-specific abstractions whose origin domain is Partial Differential Equations.

• Elliptic operator — A differential operator whose principal symbol is invertible away from the zero covector, excluding real characteristic directions and supporting strong regularity for its solutions.
• Sobolev spaces for planar domains — A Hilbert-space framework that encodes weak derivatives and boundary traces to formulate elliptic boundary-value and eigenvalue problems on bounded planar domains.