We establish a gradient estimate for very weak solution to quasilinear elliptic equation with nonstandard growth condition, which is natural generalization of the p -Laplace equation. investigate maximum extent hold without imposing any regularity assumption on nonlinearity other than basic structure assumptions. Our results also include higher integrability result and existence solutions such ...

The Laplace transform method (LTM) is introduced to solve Burgers’ equation. Because of the nonlinear term in Burgers’ equation, one cannot directly apply the LTM. Increment linearization technique is introduced to deal with the situation. This is a key idea in this paper. The increment linearization technique is the following: In time level t , we divide the solution u(x, t) into two parts: u(...

Summary: We consider the problem of estimating the first k coefficients in a regression equation with k + 1 variables. For this problem with known variance of innovations, the neutral Laplace weighted-average least-squares estimator was introduced in Magnus (2002). We investigate properties of this estimator in the case where the unknown variance is estimated by least squares. We find that the ...

Abstract—Laplace transformations have wide applications in engineering and sciences. All previous studies of modified Laplace transformations depend on differential equation with initial conditions. The purpose of our paper is to solve the linear differential equations (not initial value problem) and then find the general solution (not particular) via the Laplace transformations without needed ...

Abstract: This paper aims to apply the Laplace transform for solving linear fractional-order differential equation. The Laplace transform is a powerful tool in applied mathematics and engineering. It will allow us to transform fractional differential equations into algebraic equations and then by solving this algebraic equations, we can obtain the unknown function by using the Inverse Laplace T...

In this paper, we prove the existence of non-negative solutions for a non-local higher order degenerate parabolic equation arising in the modeling of hydraulic fractures. The equation is similar to the well-known thin film equation, but the Laplace operator is replaced by a Dirichlet-toNeumann operator, corresponding to the square root of the Laplace operator on a bounded domain with Neumann bo...

The axi-symmetric Young-Laplace differential equation is analyzed. Solutions of this equation can describe the outer or inner free surface of a static meniscus the static liquid bridge free surface between the shaper and the crystal surface occurring in single crystal tube growth. The analysis concerns the dependence of solutions of the equation on a parameter p which represents the controllabl...

During the last two decades many domain decomposition algorithms have been constructed and lot of techniques have been developed to prove the convergence of the algorithms at the continuous level. Among the techniques used to prove the convergence of classical Schwarz algorithms, the first technique is the maximum principle used by Schwarz. Adopting this technique M. Gander and H. Zhao proved a...

The main objective of this work is to introduce a novel generalization double transformations called the triple Laplace–ARA–Sumudu transform (TLARAST). This hybrid transformation extends concepts Laplace–Sumudu, Laplace–ARA and ARA–Sumudu transforms into transform. article provides definition TLARAST investigates its fundamental properties, including existence, inverses related theorems. Furthe...

The volumes, spectra and geodesics of a recently constructed infinite family of fivedimensional inhomogeneous Einstein metrics on the two S bundles over S are examined. The metrics are in general of cohomogeneity one but they contain the infinite family of homogeneous metrics T . The geodesic flow is shown to be completely integrable, in fact both the Hamilton-Jacobi and the Laplace equation se...