-Laplacian equations in with critical growth.
Natural boundary value problems for weighted form laplacians
The four natural boundary problems for the weighted form Laplacians acting on polynomial differential forms in the -dimensional Euclidean ball are solved explicitly. Moreover, an algebraic algorithm for generating a solution from the boundary data is given in each case.
Necessary And Sufficient Conditions For Existence Of Solutions To Equations With Noninvertible Linear Part.
Necessary and sufficient optimality conditions for elliptic control problems with finitely many pointwise state constraints
The goal of this paper is to prove the first and second order optimality conditions for some control problems governed by semilinear elliptic equations with pointwise control constraints and finitely many equality and inequality pointwise state constraints. To carry out the analysis we formulate a regularity assumption which is equivalent to the first order optimality conditions. Though the presence of pointwise state constraints leads to a discontinuous adjoint state, we prove that the optimal...
Necessary and sufficient optimality conditions for elliptic control problems with finitely many pointwise state constraints
The goal of this paper is to prove the first and second order optimality conditions for some control problems governed by semilinear elliptic equations with pointwise control constraints and finitely many equality and inequality pointwise state constraints. To carry out the analysis we formulate a regularity assumption which is equivalent to the first order optimality conditions. Though the presence of pointwise state constraints leads to a discontinuous adjoint state, we prove that the optimal control...
Necessary conditions of existence for an elliptic equation with source term and measure data involving -Laplacian.
Néel and Cross-Tie wall energies for planar micromagnetic configurations
We study a two-dimensional model for micromagnetics, which consists in an energy functional over -valued vector fields. Bounded-energy configurations tend to be planar, except in small regions which can be described as vortices (Bloch lines in physics). As the characteristic “exchange-length” tends to 0, they converge to planar divergence-free unit norm vector fields which jump along line singularities. We derive lower bounds for the energy, which are explicit functions of the jumps of the limit....
Néel and Cross-Tie Wall Energies for Planar Micromagnetic Configurations
We study a two-dimensional model for micromagnetics, which consists in an energy functional over S2-valued vector fields. Bounded-energy configurations tend to be planar, except in small regions which can be described as vortices (Bloch lines in physics). As the characteristic “exchange-length” tends to 0, they converge to planar divergence-free unit norm vector fields which jump along line singularities. We derive lower bounds for the energy, which are explicit functions of the jumps of the limit....
Nehari's problem and competing species systems
Neue Kriterien für das Fehlen von L2-Lösungen für -...v = f(x, v) im Rn unter besonderer Berücksichtigung des linearen Falles.
Neumann problem in a class of harmonic functions in domains with a piecewise-Lyapunov boundary.
Neumann problems associated to nonhomogeneous differential operators in Orlicz–Sobolev spaces
We study a nonlinear Neumann boundary value problem associated to a nonhomogeneous differential operator. Taking into account the competition between the nonlinearity and the bifurcation parameter, we establish sufficient conditions for the existence of nontrivial solutions in a related Orlicz–Sobolev space.
Neumann-Neumann algorithms for spectral elements in three dimensions
Neumann-Neumann methods for vector field problems.
New a priori estimates for -nonlinear elliptic systems with strong nonlinearities in the gradient, .
New and old function spaces in the theory of PDEs and nonlinear analysis
New estimates for div-curl products and very weak solutions of PDEs
New estimates for elliptic equations and Hodge type systems
We establish new estimates for the Laplacian, the div-curl system, and more general Hodge systems in arbitrary dimension , with data in . We also present related results concerning differential forms with coefficients in the limiting Sobolev space .
New exact solutions to the nonautonomous Liouville equation.
New ideas on complete integrability