Abstract
We study those nonlinear partial differential equations which appear as Euler-Lagrange equations of variational problems. On defining weak boundary values of solutions to such equations we initiate the theory of Lagrangian boundary value problems in spaces of appropriate smoothness. We also analyse if the concept of mapping degree of current importance applies to Lagrangian problems
Highlights
A Degree Theory for Lagrangian Boundary Value ProblemsReceived 08.05.2019, received in revised form 06.09.2019, accepted 06.11.2019 Abstract
Received 08.05.2019, received in revised form 06.09.2019, accepted 06.11.2019 Abstract. We study those nonlinear partial differential equations which appear as Euler-Lagrange equations of variational problems
Distribution theory steams from weak solutions of linear differential equations and it is hardly efficient for nonlinear equations
Summary
Received 08.05.2019, received in revised form 06.09.2019, accepted 06.11.2019 Abstract. We study those nonlinear partial differential equations which appear as Euler-Lagrange equations of variational problems. On defining weak boundary values of solutions to such equations we initiate the theory of Lagrangian boundary value problems in spaces of appropriate smoothness. We analyse if the concept of mapping degree of current importance applies to Lagrangian problems.
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