Non - differentiable embedding of Lagrangian systems and partial differential equations
نویسنده
چکیده
We develop the non-di erentiable embedding theory of di erential operators and Lagrangian systems using a new operator on non-di erentiable functions. We then construct the corresponding calculus of variations and we derive the associated non-di erentiable Euler-Lagrange equation, and apply this formalism to the study of PDE's. First, we extend the characteristics method to the non-di erentiable case. We prove that non-di erentiable characteristics for the Navier-Stokes equation correspond to extremals of an explicit nondi erentiable Lagrangian system. Second, we prove that the solutions of the Schrödinger equation are non-di erentiable extremals of the Newton's Lagrangian.
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