Variational Principles and Partial Differential Equations
Dirichlet’s principle consists in constructing harmonic functions by minimizing the Dirichlet integral in an appropriate class of functions. This idea is generalized, and minimizers of variational integrals are weak solutions of the associated differential equations of Euler and Lagrange. Several examples are discussed.
KeywordsPartial Differential Equation Weak Solution Variational Principle Weak Convergence Lower Semicontinuity
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