On the existence of solutions to a special variational problem

Cellina, Arrigo; Vornicescu, Mihai
June 2009
Calculus of Variations & Partial Differential Equations;Jun2009, Vol. 35 Issue 2, p263
Academic Journal
In this paper we establish an existence and regularity result for solutions to the problem for boundary data that are constant on each connected component of the boundary of O. The Lagrangean L belongs to a class that contains both extended valued Lagrangeans and Lagrangeans with linear growth. Regularity means that the solution $${\tilde w}$$ is Lipschitz continuous and that, in addition, $${\|L^\prime(|\nabla\tilde w|)\|_\infty}$$ is bounded.


Related Articles

  • THE HARDY INEQUALITY WITH ONE NEGATIVE PARAMETER. Kufner, A.; Kuliev, K.; Kulieva, G. // Banach Journal of Mathematical Analysis;2008, Vol. 2 Issue 2, p76 

    In this paper, necessary and sufficient conditions for the validity of the Hardy inequality for the case q < 0, p > 0 and for the case q > 0, p < 0 are derived.

  • THREE-PARAMETER WEIGHTED HARDY TYPE INEQUALITIES. Oinarov, R.; Kalybay, A. // Banach Journal of Mathematical Analysis;2008, Vol. 2 Issue 2, p85 

    For 0 < r < ∞ and 1 ≤ p ≤ q < ∞ we find necessary and sufficient conditions for the validity of the following inequality: (Multiple line equation(s) cannot be represented in ASCII text) where u(·), v(·), and w(·) are weight functions.

  • Regional climate model sensitivity to domain size. Leduc, Martin; Laprise, René // Climate Dynamics;Jun2009, Vol. 32 Issue 6, p833 

    Regional climate models are increasingly used to add small-scale features that are not present in their lateral boundary conditions (LBC). It is well known that the limited area over which a model is integrated must be large enough to allow the full development of small-scale features. On the...

  • A Variational Approach for a Class of Nonlinear Elliptic Boundary Value Problems. Kravvaritis, Dimitrios; Matei, Pavel; Smyrlis, George // Nonlinear Studies;2003, Vol. 10 Issue 1, p39 

    Uses the Ekeland's Variational Principle in the framework of Orlicz-Sobolev spaces to obtain the existence and uniqueness of the weak solution to a class of nonlinear elliptic boundary value problems with slowly increasing non-polynomial coefficient functions. Definitions and facts from the...

  • Capability indices and nonconforming proportion in univariate and multivariate processes. González, Isabel; Sánchez, Ismael // International Journal of Advanced Manufacturing Technology;Feb2010, Vol. 44 Issue 9/10, p1036 

    The main usefulness of a capability index is to relate the actual variability of the process with the admissible one. This admissible variability is, in turn, related with the nonconforming proportion. Hence, the capability index should be closely related to the nonconforming proportion. In...

  • Preoperative Neutrophil/Lymphocyte Ratio Predicts Overall Survival and Extravesical Disease in Patients Undergoing Radical Cystectomy. Krane, L. Spencer; Richards, Kyle A.; Kader, A. Karim; Davis, Ronald; Balaji, K.C.; Hemal, Ashok K. // Journal of Endourology;Aug2013, Vol. 27 Issue 8, p1046 

    Purpose: To evaluate if hematologic parameters and inflammatory markers could predict extravesical tumor and overall survival after radical cystectomy for patients with recurrent high grade T1 or muscle-invasive bladder cancer. Patients and Methods: A total of 68 consecutive cases of radical...

  • Homogenization for the p-Laplace operator in perforated media with nonlinear restrictions on the boundary of the perforations: A critical Case. Gómez, D.; Pérez, M.; Podolskiy, A.; Shaposhnikova, T. // Doklady Mathematics;Jul2015, Vol. 92 Issue 1, p433 

    The article presents a study on solution uε's asymptotic behavior of the variational inequality the p-Laplace operator. Topics discussed include the continuous differentiable function σ = σ(x, u), the asymptotic transformation of the values α and γ, the ε-dependent problem into...

  • Multiobjective optimization problem with variational inequality constraints. Ye, J.J.; Zhu, Qiji J. // Mathematical Programming;Apr2003, Vol. 96 Issue 1, p139 

    We study a general multiobjective optimization problem with variational inequality, equality, inequality and abstract constraints. Fritz John type necessary optimality conditions involving Mordukhovich coderivatives are derived. They lead to Kuhn-Tucker type necessary optimality conditions under...

  • Modified H-R mixed variational principle for magnetoelectroelastic bodies and state-vector equation. Guang-hui, Qing; Jia-jun, Qiu; Yan-hong, Liu // Applied Mathematics & Mechanics;Jun2005, Vol. 26 Issue 6, p722 

    Based upon the Hellinger-Reissner (H-R) mixed variational principle for three-dimensional elastic bodies, the modified H-R mixed variational theorem for magnetoelectroelastic bodies was established. The state-vector equation of magnetoelectroelastic plates was derived from the proposed theorem...


Read the Article


Sign out of this library

Other Topics