A note on the parabolic differential and difference equations.
A note on the parabolic variation
A condition for solvability of an integral equation which is connected with the first boundary value problem for the heat equation is investigated. It is shown that if this condition is fulfilled then the boundary considered is -Holder. Further, some simple concrete examples are examined.
A note on the Poisson-Boltzmann equation
A Note on the Problem -...u = ...u + u| u|2*-2.
A note on the regularity of autonomous quasilinear elliptic and parabolic systems
A note on the regularity of solutions of Hamilton-Jacobi equations with superlinear growth in the gradient variable
We investigate the regularity of solutions of first order Hamilton-Jacobi equation with super linear growth in the gradient variable. We show that the solutions are locally Hölder continuous with Hölder exponent depending only on the growth of the hamiltonian. The proof relies on a reverse Hölder inequality.
A note on the regularity of solutions of Hamilton-Jacobi equations with superlinear growth in the gradient variable
We investigate the regularity of solutions of first order Hamilton-Jacobi equation with super linear growth in the gradient variable. We show that the solutions are locally Hölder continuous with Hölder exponent depending only on the growth of the Hamiltonian. The proof relies on a reverse Hölder inequality.
A note on the regularity of the degenerate complex Monge-Ampère equation
We prove the almost regularity of the degenerate complex Monge-Ampère equation in a special case.
A note on the regularity of the solutions to two variational inequalities involving a pseudodifferential operator.
A note on the relaxation-time limit of the isothermal Euler equations.
A note on the Rellich formula in Lipschitz domains.
Let L be a symmetric second order uniformly elliptic operator in divergence form acting in a bounded Lipschitz domain Ω of RN and having Lipschitz coefficients in Ω. It is shown that the Rellich formula with respect to Ω and L extends to all functions in the domain D = {u ∈ H01(Ω); L(u) ∈ L2(Ω)} of L. This answers a question of A. Chaïra and G. Lebeau.
A note on the Robin problem in potential theory (Preliminary communication)
A note on the shift theorem for the Laplacian in polygonal domains
We present a shift theorem for solutions of the Poisson equation in a finite planar cone (and hence also on plane polygons) for Dirichlet, Neumann, and mixed boundary conditions. The range in which the shift theorem holds depends on the angle of the cone. For the right endpoint of the range, the shift theorem is described in terms of Besov spaces rather than Sobolev spaces.
A note on the solution of the von Kármán equations using series and Chebyshev spectral methods.
A note on the solvability of nonlinear elliptic problems with jumping nonlinearities
A note on the unique solvability of an inverse problem with integral overdetermination.
A Note on the Uniqueness and Structure of Solutions to the Dirichlet Problem for Some Elliptic Systems
In this note, we consider some elliptic systems on a smooth domain of . By using the maximum principle, we can get a more general and complete results of the identical property of positive solution pair, and thus classify the structure of all positive solutions depending on the nonlinarities easily.
A note on the uniqueness of entropy solutions to first order quasilinear equations.
A note on the variational structure of an elliptic system involving critical Sobolev exponent.
A note on two dimensional Bratu problem