A generalization of the maximum principle to nonlinear parabolic systems
A generalization of the well-known weak maximum principle is established for a class of quasilinear strongly coupled parabolic systems with leading terms of p-Laplacian type.
A generalized Fuc̆ik type eigenvalue problem for p-Laplacian.
A generalized maximum principle and estimates of max vrai for nonlinear parabolic boundary value problems
A generalized maximum principle for boundary value problems for degenerate parabolic operators with discontinuous coefficients
We prove a generalized maximum principle for subsolutions of boundary value problems, with mixed type unilateral conditions, associated to a degenerate parabolic second-order operator in divergence form.
A generalized strange term in Signorini’s type problems
The limit behavior of the solutions of Signorini’s type-like problems in periodically perforated domains with period is studied. The main feature of this limit behaviour is the existence of a critical size of the perforations that separates different emerging phenomena as . In the critical case, it is shown that Signorini’s problem converges to a problem associated to a new operator which is the sum of a standard homogenized operator and an extra zero order term (“strange term”) coming from the...
A Generalized Strange Term in Signorini's Type Problems
The limit behavior of the solutions of Signorini's type-like problems in periodically perforated domains with period ε is studied. The main feature of this limit behaviour is the existence of a critical size of the perforations that separates different emerging phenomena as ε → 0. In the critical case, it is shown that Signorini's problem converges to a problem associated to a new operator which is the sum of a standard homogenized operator and an extra zero order term (“strange term”) coming from...
A geometric analysis of a singular ODE related to the study of a quasilinear PDE.
A geometric and analytic approach to some problems associated with Emden equations
A geometric approach to invariant sets for dynamical systems.
A geometric improvement of the velocity-pressure local regularity criterion for a suitable weak solution to the Navier-Stokes equations
We deal with a suitable weak solution to the Navier-Stokes equations in a domain . We refine the criterion for the local regularity of this solution at the point , which uses the -norm of and the -norm of in a shrinking backward parabolic neighbourhood of . The refinement consists in the fact that only the values of , respectively , in the exterior of a space-time paraboloid with vertex at , respectively in a ”small” subset of this exterior, are considered. The consequence is that...
A global attractor in a general diffusive food chain model.
A global bifurcation result of a Neumann problem with indefinite weight.
A global branch of steady vortex rings.
A Global Compactness Result for Elliptic Boundary Value Problems Involving Limiting Nonlinearities.
A global continuation theorem for obtaining eigenvalues and bifurcation points
A global differentiability result for solutions of nonlinear elliptic problems with controlled growths
Let be a bounded open subset of , . In we deduce the global differentiability result for the solutions of the Dirichlet problem with controlled growth and nonlinearity . The result was obtained by first extending the interior differentiability result near the boundary and then proving the global differentiability result making use of a covering procedure.
A global existence-global nonexistence conjecture of Fujita type for a system of degenerate semilinear parabolic equations
A global solution curve for a class of semilinear equations.
A gradient estimate for solutions of the heat equation
A gradient estimate for solutions of the heat equation. II
The author obtains an estimate for the spatial gradient of solutions of the heat equation, subject to a homogeneous Neumann boundary condition, in terms of the gradient of the initial data. The proof is accomplished via the maximum principle; the main assumption is that the sufficiently smooth boundary be convex.