Conservation laws from any conformal transformations and the parameters for a sharp V-notch in plane elasticity

► Two new independent Lagrangian functions are presented for plane elasticity. ► Conservation integral in Noether's sense includes any conformal transformation. ► A finite value can be obtained due to any conformal transformation. ► Two parameters for a sharp V-notch in Mode I and II problems are presented. ► Two parameters are equivalent to the NSIFs.