Abdelali Sabri, Ahmed Jamea, Hamad Talibi Alaoui (2022)
Mathematica Bohemica
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In the present paper, we prove the existence and uniqueness of weak solution to a class of nonlinear degenerate elliptic $p$-Laplacian problem with Dirichlet-type boundary condition, the main tool used here is the variational method combined with the theory of weighted Sobolev spaces.
G. A. Afrouzi, A. Hadjian, S. Heidarkhani (2013)
Annales Polonici Mathematici
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We prove the existence of at least one non-trivial solution for Dirichlet quasilinear elliptic problems. The approach is based on variational methods.
I. Birindelli, F. Demengel (2014)
ESAIM: Control, Optimisation and Calculus of Variations
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We prove Hölder regularity of the gradient, up to the boundary for solutions of some fully-nonlinear, degenerate elliptic equations, with degeneracy coming from the gradient.
Arkhipova, A. (2004)
Zapiski Nauchnykh Seminarov POMI
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Jan Bęczek (1988)
Annales Polonici Mathematici
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N. Kutev (1987)
Banach Center Publications
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Juan J. Nieto (1990)
Commentationes Mathematicae Universitatis Carolinae
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J. R. Whiteman, M. Aslam Noor (1976)
Publications mathématiques et informatique de Rennes
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Arkhipova, A.A. (2004)
Journal of Mathematical Sciences (New York)
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G. Barles (1988)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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Marek Galewski (2003)
Annales Polonici Mathematici
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A new variational principle and duality for the problem Lu = ∇G(u) are provided, where L is a positive definite and selfadjoint operator and ∇G is a continuous gradient mapping such that G satisfies superquadratic growth conditions. The results obtained may be applied to Dirichlet problems for both ordinary and partial differential equations.
Aleksandra Orpel (2004)
Banach Center Publications
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We investigate the existence of solutions for the Dirichlet problem including the generalized balance of a membrane equation. We present a duality theory and variational principle for this problem. As one of the consequences of the duality we obtain some numerical results which give a measure of a duality gap between the primal and dual functional for approximate solutions.
Michal Křížek, Liping Liu (1996)
Applicationes Mathematicae
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A nonlinear elliptic partial differential equation with the Newton boundary conditions is examined. We prove that for greater data we get a greater weak solution. This is the so-called comparison principle. It is applied to a steady-state heat conduction problem in anisotropic magnetic cores of large transformers.
Masashi Misawa (2004)
Applicationes Mathematicae
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We study the existence of a weak solution to a Cauchy-Dirichlet problem for evolutional p-Laplacian systems with constant coefficients and principal term only. The initial-boundary data is assumed to be a bounded weak solution of an evolutional p-Laplacian system with an L¹-function as external force. The key ingredient is the maximum principle for weak solutions.
Paweł Goldstein, Paweł Strzelecki, Anna Zatorska-Goldstein (2013)
Studia Mathematica
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We consider a class of fourth order elliptic systems which include the Euler-Lagrange equations of biharmonic mappings in dimension 4 and we prove that a weak limit of weak solutions to such systems is again a weak solution to a limit system.