College of Arts and Sciences (CAS)College of Arts and Scienceshttp://hdl.handle.net/11073/83902022-12-05T07:52:14Z2022-12-05T07:52:14ZMaximum principles and overdetermined problems for Hessian equationsEnache, CristianMarras, MonicaPorru, Giovannihttp://hdl.handle.net/11073/250832022-11-17T23:02:24Z2021-01-01T00:00:00ZMaximum principles and overdetermined problems for Hessian equations
Enache, Cristian; Marras, Monica; Porru, Giovanni
In this article we investigate some Hessian type equations. Our main aim is to derive new maximum principles for some suitable P-functions, in the sense of L.E. Payne, that is for some appropriate functional combinations of u(x) and its derivatives, where u(x) is a solution of the given Hessian type equations. To find the most suitable P-functions, we first investigate the special case of a ball, where the solution of our Hessian equations is radial, since this case gives good hints on the best functional to be considered later, for general domains. Next, we construct some elliptic inequalities for the well-chosen P-functions and make use of the classical maximum principles to get our new maximum principles. Finally, we consider some overdetermined problems and show that they have solutions when the underlying domain has a certain shape (spherical or ellipsoidal).
2021-01-01T00:00:00ZRenormalization functions of the tricritical O(N)-symmetricΦ⁶ model beyond the next-to-leading order in 1/NSakhi, Saidhttp://hdl.handle.net/11073/250822022-11-17T23:02:29Z2021-01-01T00:00:00ZRenormalization functions of the tricritical O(N)-symmetricΦ⁶ model beyond the next-to-leading order in 1/N
Sakhi, Said
We investigate higher-order corrections to the effective potential of the tricritical O(N)-symmetric Φ⁶ model in 3-2ε dimensions in its phase exhibiting spontaneous breaking of its scale symmetry. The renormalization group β-function and the anomalous dimension γ of this model are computed up to the next-to-next-to-leading order in the 1/N expansion technique and using a dimensional regularization in a minimal subtraction scheme.
2021-01-01T00:00:00ZFractional Integrodifferentiation and Toeplitz Operators with Vertical SymbolsKarapetyants, AlexeyLouhichi, Issamhttp://hdl.handle.net/11073/250782022-11-11T23:02:29Z2020-01-01T00:00:00ZFractional Integrodifferentiation and Toeplitz Operators with Vertical Symbols
Karapetyants, Alexey; Louhichi, Issam
We consider the so-called vertical Toeplitz operators on the weighted Bergman space over the half plane. The terminology “vertical” is motivated by the fact that if a is a symbol of such Toeplitz operator, then a(z) depends only on y = ℑz, where z = x + iy. The main question raised in this paper can be formulated as follows: given two bounded vertical Toeplitz operators Tλa and Tλb, under which conditions is there a symbol h such that TλaTλb=Tλh? It turns out that this problem has a very nice connection with fractional calculus! We shall formulate our main results using the well-known theory of Riemann–Liouville fractional integrodifferentiation.
2020-01-01T00:00:00ZOn the powers of quasihomogeneous Toeplitz operatorsAissa, BouhaliZohra, BendaoudLouhichi, Issamhttp://hdl.handle.net/11073/250772022-11-11T23:02:30Z2021-01-01T00:00:00ZOn the powers of quasihomogeneous Toeplitz operators
Aissa, Bouhali; Zohra, Bendaoud; Louhichi, Issam
In this article, a fixed point iterative scheme involving Green's function is applied to reach a solution for the buckling of nano-actuators under nonlinear forces. Our solution is convergent. The nano-actuators problem under consideration is governed by a general type equation that contains nonlinear forces and integro-differential terms. The equation, we adopted and which governs the nano-actuators, is a nonlinear integro-differential BVP of fourth order. Our scheme enjoys important features such as high accuracy, robustness, and fast convergence. Numerical tests are performed and compared with other results that exist in the current literature.
2021-01-01T00:00:00Z