Oblique derivative problems in Lipschitz domains: II. Discontinuous boundary data.
On a class of Monge-Ampére problems with non-homogeneous Dirichlet boundary condition.
On a maximum principle for elliptic systems with constant coefficients
On a maximum principle for weak solutions of the stationary Stokes system
On a nonlinear eigenvalue problem in Sobolev spaces with variable exponent.
On maximum principle for weak subsolutions of degenerate parabolic linear equations
Sufficient conditions are obtained so that a weak subsolution of , bounded from above on the parabolic boundary of the cylinder , turns out to be bounded from above in .
On maximum principles and Liouville theorems for quasilinear elliptic equations and systems
On principal eigenvalues for periodic parabolic Steklov problems.
On solutions of the exterior Dirichlet problem for the minimal surface equation
On solvability of boundary value problem for elliptic equations with Bitsadze-Samarskij condition.
On some properties of solutions of the Cauchy problem for a quasilinear parabolic equation
On the antimaximum principle for parabolic periodic problems with weight.
On the Dirichlet problem for a second order elliptic system with degeneration on the entire domain boundary.
On the existence of positive solutions for periodic parabolic sublinear problems.
On the First Eigenvalue of Non-Uniformly Elliptic Boundary Value Problems.
On the global existence for the Muskat problem
The Muskat problem models the dynamics of the interface between two incompressible immiscible fluids with different constant densities. In this work we prove three results. First we prove an maximum principle, in the form of a new “log” conservation law which is satisfied by the equation (1) for the interface. Our second result is a proof of global existence for unique strong solutions if the initial data is smaller than an explicitly computable constant, for instance . Previous results of this...
On the Keldyš-Fichera boundary-value problem for degenerate quasilinear elliptic equations.
On the -regularity of solutions of nonlinear elliptic equations in Orlicz spaces.
On the maximum modulus theorem for the Stokes system
On the maximum principle for principal curvatures
The paper contains the estimates from above of the principal curvatures of the solution to some curvature equations. A correction of the author's previous argument is presented.