Abstract
We prove the existence of solutions for an elliptic partial differential equation having more general flux term than either -Laplacian or flux term of the Leray-Lions type conditions: . Brouwer's fixed point theorem is one of the fundamental tools of the proof.
Highlights
We are concerned with problems of partial differential equations such as a nonlinear elliptic equation−∇ · J f, 1.1 which contains the flux term J
We prove the existence of solutions for an elliptic partial differential equation having more general flux term than either p-Laplacian or flux term of the Leray-Lions type conditions:
The flux term J is a vector field that explains a movement of some physical contents u such as temperature, chemical potential, electrostatic potential, or fluid flows
Summary
−∇ · J f, 1.1 which contains the flux term J. We introduce a new function space which is designed to handle solutions of nonlinear equations 1.3. This space is arisen from a close look at the Lp-norm f Lp of the classical Lebesgue spaces Lp X , 1 ≤ p < ∞. For nonlinear problems such as 1.3 , the homogeneity property may not be an essential factor— we try to explain that the new space accommodates the solutions of nonlinear problems without homogeneity. This space is similar to the Orlicz spaces, we present a different approach of discovering the new spaces which generalize the space Lp
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
