Analysis of Weighted Sobolev Space Solutions for Nonlinear Capillarity Problem with Dirichlet Boundary Conditions
Main Article Content
Abstract
This work establishes the existence of weak solutions for p-Laplacian-like equations in weighted Sobolev spaces under Dirichlet boundary conditions, assuming the data is in the weighted Lebesgue space.
Article Details
References
- I. Aydin, Weighted Variable Sobolev Spaces and Capacity, J. Funct. Spaces Appl. 2012 (2012), 132690. https://doi.org/10.1155/2012/132690.
- M. Chipot, Elliptic Equations: An Introductory Course, Birkhäuser, Basel, 2009. https://doi.org/10.1007/978-3-7643-9982-5.
- P. Drábek, A. Kufner, F. Nicolosi, Nonlinear Elliptic Equations, Singular and Degenerate Cases, Preprint, University of West Bohemia, 1996.
- L. Hmidouch, A. Jamea, M. Laghdir, Existence of Entropy Solution for a Nonlinear Parabolic Problem in Weighted Sobolev Space via Optimization Method, Math. Model. Anal. 28 (2023), 393–414. https://doi.org/10.3846/mma.2023.17010.
- J. Heinonen, T. Kilpeläinen, O. Martio, Nonlinear Potential Theory of Degenerate Elliptic Equations, Dover Publications, Mineola, 2006.
- J.L. Lions, Quelques Methodes de Résolution des Problèmes aux Limites Non Linéaires, Dunod, Paris, 1969.
- W.M. Ni, J. Serrin, Non-Existence Theorems for Quasilinear Partial Differential Equations, Rend. Circ. Mat. Palermo 2 Suppl. 8 (1985), 171–185.
- W.M. Ni, J. Serrin, Existence and Nonexistence Theorems for Ground States for Quasilinear Partial Differential Equations, Accad. Naz. dei Lincei 77 (1986), 231–257.
- M.M. Rodrigues, Multiplicity of Solutions on a Nonlinear Eigenvalue Problem for p(x)-Laplacian-like Operators, Mediterr. J. Math. 9 (2012), 211–223. https://doi.org/10.1007/s00009-011-0115-y.
- S. Shokooh, G.A. Afrouzi, S. Heidarkhani, Multiple Solutions for P(X)-Laplacian-Like Problems With Neumann Condition, Acta Univ. Apulensis 49 (2017), 111–128.
- B.O. Turesson, Nonlinear Potential Theory and Weighted Sobolev Spaces, Springer, Berlin, 2000.