This paper brings together methods to solve and/or characterize solutions of some problems mathematical physics equations involving p-Laplacian and p-pseudo-Laplacian. Using surjectivity or variational approaches, one may obtain weak for Dirichlet Newmann these important operators. article details three ways use results a special type operator the duality mapping Nemytskii operator, starting fr...

In this work, we consider the Cauchy problem for u′ − Au = f with A the Laplacian operator on some Riemannian manifolds or a sublapacian on some Lie groups or some second order elliptic operators on a domain. We show the boundedness of the operator of maximal regularity f 7→ Au and its adjoint on appropriate Hardy spaces which we define and study for this purpose. As a consequence we reobtain t...

The paper addresses existence, uniqueness and approximation methods for a certain class of nonlinear parabolic quasi-variational inequality (QVI) problems with special gradient-type constraints. Problems of this nature are common in the mathematical modeling of superconductors and ionization in electrostatics. The results are developed based on monotone operator theory , C 0 semigroup methods a...

Abstract We study the existence and multiplicity of weak solutions for an elliptic problem involving $p(x)$ p(x) -Laplacian operator under Steklov boundary condition. The approach is based on variational methods.

The game-theoretic p-Laplacian operator is a version of classical variational which in connection with stochastic games called Tug-of-War noise. existence positive singular and Holder continuous solutions the p-Laplace involving gradient small C2 perturbation unit ball Rn are proved. Finally, more case problem introduced.

Classical Yang–Mills theory in four dimensions is studied by using the Coulomb gauge, as a first step towards considering the mass gap problem in the quantum theory. The Coulomb gauge Hamiltonian involves integration of matrix elements of an operator P which is studied both at perturbative and at non-perturbative level. Upon replacing space-time by a compact Riemannian 4-manifold without bounda...