Lax–Milgram Theorem
A bounded coercive bilinear form gives a unique solution for each continuous linear functional. The elliptic application shows how adding a sufficiently large zeroth-order term can restore coercivity.
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Hilbert Space · continuous dual space · Weak Solution of a PDE
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Start here: Notes on Partial Differential Equations
John K. Hunter · Lecture notes · English · Free full text
§4.7 The Lax-Milgram theorem and general elliptic PDEs, Theorems 4.20–4.22
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Differential Equations & PDEs in the library · Preparation and skip guidance