Une caractérisation des opérateurs elliptiques autoadjoints
Unicité pour le problème de Cauchy à partir d'une surface partout caractéristique ; applications
Uniform analytic-Gevrey regularity of solutions to a semilinear heat equation
We study the Gevrey regularity down to t = 0 of solutions to the initial value problem for a semilinear heat equation . The approach is based on suitable iterative fixed point methods in based Banach spaces with anisotropic Gevrey norms with respect to the time and the space variables. We also construct explicit solutions uniformly analytic in t ≥ 0 and x ∈ ℝⁿ for some conservative nonlinear terms with symmetries.
Uniqueness and regularity properties of linear operators and their applications
Viscosity solutions of nonlinear systems of degenerated elliptic equations of second order.
Weak uniqueness and partial regularity for the composite membrane problem
We study the composite membrane problem in all dimensions. We prove that the minimizing solutions exhibit a weak uniqueness property which under certain conditions can be turned into a full uniqueness result. Next we study the partial regularity of the solutions to the Euler–Lagrange equation associated to the composite problem and also the regularity of the free boundary for solutions to the Euler–Lagrange equations.
Weak-strong uniqueness for Navier-Stokes/Allen-Cahn system
The coupled Navier-Stokes/Allen-Cahn system is a simple model to describe phase separation in two-component systems interacting with an incompressible fluid flow. We demonstrate the weak-strong uniqueness result for this system in a bounded domain in three spatial dimensions which implies that when a strong solution exists, then a weak solution emanating from the same data coincides with the strong solution on its whole life span. The proof of given assertion relies on a form of a relative entropy...
Weighted Miranda-Talenti inequality and applications to equations with discontinuous coefficients
Let be an open bounded set in , with boundary, and (, ) be a weighted Morrey space. In this note we prove a weighted version of the Miranda-Talenti...
Well-posedness and regularity for a parabolic-hyperbolic Penrose-Fife phase field system
This work is concerned with the study of an initial boundary value problem for a non-conserved phase field system arising from the Penrose-Fife approach to the kinetics of phase transitions. The system couples a nonlinear parabolic equation for the absolute temperature with a nonlinear hyperbolic equation for the phase variable , which is characterized by the presence of an inertial term multiplied by a small positive coefficient . This feature is the main consequence of supposing that the response...
Well-posedness and regularity results for a dynamic von Kármán plate.
Well-posedness of the Cauchy problem for hyperbolic equations with non-Lipschitz coefficients.
Well-posedness results for a model of damage in thermoviscoelastic materials
When does the free boundary enter into corner points of the fixed boundary?
Wiener criterion for degenerate elliptic obstacle problem
We give a Wiener criterion for the continuity of an obstacle problem relative to an elliptic degenerate problem with a weight in the class.
Гельдеровские оценки для квазилинейных вырождающихся параболических систем второго порядка
Гладкость обобщенных решений уравнения с непрерывными коэффициентами
Дифференцируемые решения симметричных систем в плоских областях с нерегулярной границей
Задача с наклонной производной для квазилинейного параболического уравнения
Классическая разрешимость задачи Дирихле для уравнения Монжа-Ампера
Метод квазиоднородных функций и задача Фока