Ngoc Cuong Nguyen

Abstract We study the discrete and discrete fractional representation of a pharmacokinetics - pharmacodynamics (PK-PD) model describing tumor growth and anti-cancer effects in continuous time considering a time scale <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>h</m:mi> <m:msubsup> <m:mrow> <m:mi>ℕ</m:mi> </m:mrow> <m:mn>0</m:mn> <m:mi>h</m:mi> </m:msubsup> </m:mrow> </m:math> $h\mathbb{N}_0^h$ , where h &gt; 0. Since the measurements of the tumor volume in mice were take

We prove the Hölder continuity of the solution to complex Hessian equation with the right hand side in L p , $p>\frac {n}{m}$ , 1 < m < n, in a m-strongly pseudoconvex domain in ℂ n under some additional conditions on the density near the boundary and on the boundary data.

We prove the subsolution theorem for a complex Hessian equation in a smoothly bounded strongly m-pseudoconvex domain in Cn.

We prove the existence of weak solutions of complex $m$ -Hessian equations on compact Hermitian manifolds for the non-negative right-hand side belonging to $L^{p}$ , $p&gt;n/m$ ( $n$ is the dimension of the manifold). For smooth, positive data the equation has recently been solved by Székelyhidi and Zhang. We also give a stability result for such solutions.

Abstract We study the h -discrete and h -discrete fractional representation of a pharmacokinetics-pharmacodynamics (PK-PD) model describing tumor growth and anticancer effects in continuous time considering a time scale h 𝕅 0 , where h &gt; 0. Since the measurements of the drug concentration in plasma were taken hourly, we consider h = 1/24 and obtain the model in discrete time (i.e. hourly). We then continue with fractionalizing the h -discrete nabla operator in the h -discrete model to obtain

We give a necessary and sufficient condition for positive Borel measures such that the Dirichlet problem, with zero boundary data, for the complex Monge–Ampère equation admits Hölder continuous plurisubharmonic solutions. In particular, when the subsolution has finite Monge–Ampère total mass, we obtain an affirmative answer to a question of Zeriahi et al. (Complex Var. Elliptic Equ. 61(7):902–930, 2016).

We show that a positive Borel measure of positive finite total mass, on a compact Hermitian manifold, admits a Hölder continuous quasi-plurisubharmonic solution to the Monge–Ampère equation if and only if it is dominated locally by Monge–Ampère measures of Hölder continuous plurisubharmonic functions.

We solve the classical Dirichlet problem for a general complex Hessian equation on a small ball in C n . Then, we show that there is a continuous solution, in pluripotential theory sense, to the Dirichlet problem on compact Hermitian manifolds with boundary that equipped locally conformal Khler metrics, provided a subsolution.

Abstract We prove that if the modulus of continuity of a plurisubharmonic subsolution satisfies a Dini-type condition then the Dirichlet problem for the complex Monge-Ampère equation has the continuous solution. The modulus of continuity of the solution also given if the right hand side is locally dominated by capacity.

Abstract We study weak quasi-plurisubharmonic solutions to the Dirichlet problem for the complex Monge–Ampère equation on a general Hermitian manifold with non-empty boundary. We prove optimal subsolution theorems: for bounded and Hölder continuous quasi-plurisubharmonic functions. The continuity of the solution is proved for measures that are well dominated by capacity, for example measures with $$L^p$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>L</mml:mi><mml:mi

Abstract We prove the existence of a continuous quasi-plurisubharmonic solution to the Monge–Ampère equation on a compact Hermitian manifold for a very general measure on the right hand side. We admit measures dominated by capacity in a certain manner, in particular, moderate measures studied by Dinh–Nguyen–Sibony. As a consequence, we give a characterization of measures admitting Hölder continuous quasi-plurisubharmonic potential, inspired by the work of Dinh–Nguyen.

Let X $X$ be a compact Kähler manifold of dimension n $n$ and ω $\omega$ a Kähler form on X $X$ . We consider the complex Monge–Ampère equation ( d d c u + ω ) n = μ $({dd^c}u+\omega )^n=\mu$ , where μ $\mu$ is a given positive measure on X $X$ of suitable mass and u $u$ is an ω $\omega$ -plurisubharmonic function. We show that the equation admits a Hölder continuous solution if and only if the measure μ $\mu$ , seen as a functional on a complex Sobolev space W ∗ ( X ) $W^*(X)$ , is Hölder conti