Linear elliptic operators with measurable coefficients
Linear flow in porous media with double periodicity.
Linear hyperbolic problems in the whole scale of Sobolev-type spaces of periodic functions
We study one-dimensional linear hyperbolic systems with -coefficients subjected to periodic conditions in time and reflection boundary conditions in space. We derive a priori estimates and give an operator representation of solutions in the whole scale of Sobolev-type spaces of periodic functions. These spaces give an optimal regularity trade-off for our problem.
Linear Oblique Derivative Problems for the Uniformly Elliptic Hamilton-Jacobi-Bellman Equation.
Linear Pfaff systems with the lower characteristic vectors' set of positive Lebesgue measure.
Linear stability theory of solitary waves arising from Hamiltonian systems with symmetry
Line-energy Ginzburg-Landau models : zero-energy states
We consider a class of two-dimensional Ginzburg-Landau problems which are characterized by energy density concentrations on a one-dimensional set. In this paper, we investigate the states of vanishing energy. We classify these zero-energy states in the whole space: They are either constant or a vortex. A bounded domain can sustain a zero-energy state only if the domain is a disk and the state a vortex. Our proof is based on specific entropies which lead to a kinetic formulation, and on a careful...
Liouville results for -Laplace equations of Lane-Emden-Fowler type
Liouville theorems, a priori estimates, and blow-up rates for solutions of indefinite superlinear parabolic problems
In this paper we establish new nonlinear Liouville theorems for parabolic problems on half spaces. Based on the Liouville theorems, we derive estimates for the blow-up of positive solutions of indefinite parabolic problems and investigate the complete blow-up of these solutions. We also discuss a priori estimates for indefinite elliptic problems.
Liouville theorems and blow up behaviour in semilinear reaction diffusion systems
Liouville theorems based on symmetric diffusions
Liouville theorems for a class of linear second-order operators with nonnegative characteristic form.
Liouville Theorems for Nondiagonal Elliptic Systems in Arbitrary Dimensions.
Liouville Theorems for Nonlinear Elliptic Equations and Systems.
Liouville type condition and the interior regularity of quasilinear parabolic system (the case of BMO-solutions)
Liouville type results for periodic and almost periodic linear operators
Liouville type theorem for solutions of linear partial differential equations with constant coefficients
We discuss existence of global solutions of moderate growth to a linear partial differential equation with constant coefficients whose total symbol P(ξ) has the origin as its only real zero. It is well known that for such equations, global solutions tempered in the sense of Schwartz reduce to polynomials. This is a generalization of the classical Liouville theorem in the theory of functions. In our former work we showed that for infra-exponential growth the corresponding assertion is true if and...
Liouville type theorems for some conformally invariant fully nonlinear equations
This is a report on some joint work with Aobing Li on Liouville type theorems for some conformally invariant fully nonlinear equations.
Liouville type theorems for φ-subharmonic functions.
In this paper we present some Liouville type theorems for solutions of differential inequalities involving the φ-Laplacian. Our results, in particular, improve and generalize known results for the Laplacian and the p-Laplacian, and are new even in these cases. Phragmen-Lindeloff type results, and a weak form of the Omori-Yau maximum principle are also discussed.
Liouville-Gelfand type problems for the -laplacian on bounded domains of