Two maximum principles for a nonlinear fourth order equation from thin plate theory

Weighted biharmonic equations involving continous potentiel under exponential nonlinear growth

“…In general the study of fourth order partial differential equations is considered an interesting topic. The interest in studying such equations was stimulated by their applications in micro-electro-mechanical systems, phase field models of multi-phase systems, thin film theory, surface diffusion on solids, interface dynamics, flow in Hele-Shaw cells, see [16,20,30]. However many applications are generated by the weighted elliptic problems, such as the study of traveling waves in suspension bridges, radar imaging (see, for example [4,26]).…”

On ap(⋅)-biharmonic problem with no-flux boundary condition

“…Fourth order PDEs have various applications, to micro-electro-mechanical systems, phase field models of multiphase systems, thin film theory, thin plate theory, surface diffusion on solids, interface dynamics, flow in Hele-Shaw cells, see for example [17,24,38]. Therefore many authors focused on the study of such problems with constant exponents, like Molica Bisci and Repovš [37], Candito and Molica Bisci [12], or Liu and Squassina [35] etc.…”

A Maximum Principle Result for a General Fourth Order Semilinear Elliptic Equation

“…In this work, functionals containing the terms 2 , , i i u u u ∇ − ∆ are utilized and apriori bounds on the integral of the square of the second gradient and on the square of the gradient of the solution are deduced. Since then, many authors [2]- [11] and references therein have used this technique to obtain maximum principle results for other fourth order elliptic differential equations whose principal part is the biharmonic operator.…”

“…Other works deal with the more general fourth order elliptic operator In [12], Dunninger mentions that functionals containing the term ( ) 2 Lu can be used to obtain maximum principle results for such linear equations as A similar approach is taken in [13] for a class of nonlinear fourth order equations. In this paper, we modify the results in [1] and a matrix result from [14] to deduce maximum principles defined on the solutions to semilinear fourth order elliptic equations of the form:…”