Weak Solutions to a Landau–Lifshitz Equation with a <math xmlns='http://www.w3.org/1998/Math/MathML' id='M1'> <mi>p</mi> </math>-Laplacian Operator as an Exchange Field

We are dealing with the classical Landau–Lifshitz equation with an unusual exchange field expressed in terms of a p -Laplacian operator for p greater than 2. We obtain weak solutions to the model by using penalization, compactness arguments, and monotonicity method.