Oblique derivative problems in Lipschitz domains: II. Discontinuous boundary data.
Observations on quasi-linear partial differential equations
Observations on estimates for divergence elliptic equations with VMO coefficients
In this paper, we make some observations on the work of Di Fazio concerning estimates, , for solutions of elliptic equations , on a domain with Dirichlet data whenever and . We weaken the assumptions allowing real and complex non-symmetric operators and boundary. We also consider the corresponding inhomogeneous Neumann problem for which we prove the similar result. The main tool is an appropriate representation for the Green (and Neumann) function on the upper half space. We propose...
Obstacle problems for scalar conservation laws
In this paper we are interested in bilateral obstacle problems for quasilinear scalar conservation laws associated with Dirichlet boundary conditions. Firstly, we provide a suitable entropy formulation which ensures uniqueness. Then, we justify the existence of a solution through the method of penalization and by referring to the notion of entropy process solution due to specific properties of bounded sequences in . Lastly, we study the behaviour of this solution and its stability properties with...
Obstacle problems for scalar conservation laws
In this paper we are interested in bilateral obstacle problems for quasilinear scalar conservation laws associated with Dirichlet boundary conditions. Firstly, we provide a suitable entropy formulation which ensures uniqueness. Then, we justify the existence of a solution through the method of penalization and by referring to the notion of entropy process solution due to specific properties of bounded sequences in L∞. Lastly, we study the behaviour of this solution and its stability properties...
On a Bernoulli problem with geometric constraints
A Bernoulli free boundary problem with geometrical constraints is studied. The domain Ω is constrained to lie in the half space determined by x1 ≥ 0 and its boundary to contain a segment of the hyperplane {x1 = 0} where non-homogeneous Dirichlet conditions are imposed. We are then looking for the solution of a partial differential equation satisfying a Dirichlet and a Neumann boundary condition simultaneously on the free boundary. The existence and uniqueness of a solution have already been addressed...
On a boundary value problem for an equation of the type of non-stationary filtration
On a class of Markov type semigroups in spaces of uniformly continuous and bounded functions
We study a new class of Markov type semigroups (not strongly continuous in general) in the space of all real, uniformly continuous and bounded functions on a separable metric space E. Our results allow us to characterize the generators of Markov transition semigroups in infinite dimensions such as the heat and the Ornstein-Uhlenbeck semigroups.
On a class of nonlinear ellipticequations in Hilbert spaces
We consider elliptic nonlinear equations in a separable Hilbert space and their solutions in spaces of Sobolev type.
On a class of nonlocal nonlinear elliptic problems
On a Class of Retarded Partial Differential Equations.
On a convex combination of solutions to elliptic variational inequalities.
On a differential inequality for a viscous compressible heat conducting capillary fluid bounded by a free surface
We derive a global differential inequality for solutions of a free boundary problem for a viscous compressible heat concluding capillary fluid. The inequality is essential in proving the global existence of solutions.
On a differential inequality for equations of a viscous compressible heat conducting fluid bounded by a free surface
We derive a global differential inequality for solutions of a free boundary problem for a viscous compressible heat conducting fluid. The inequality is essential in proving the global existence of solutions.
On a fractional Nirenberg problem. Part I: Blow up analysis and compactness of solutions
We prove some results on the existence and compactness of solutions of a fractional Nirenberg problem. The crucial ingredients of our proofs are the understanding of the blow up profiles and a Liouville theorem.
On a free boundary problem associated with combustion and solidification
On a free boundary problem for minimal surfaces.
On a functional differential equation arising in the theory of the distribution of wealth.
On a general type of -adic parabolic equations.
On a hyperbolic coefficient inverse problem via partial dynamic boundary measurements.